  We report the detection of fulvenallene ($c$-C$_5$H$_4$CCH$_2$) in the
direction of TMC-1 with the QUIJOTE line survey. Thirty rotational transitions
with $K_a$=0,1,2,3 and $J$=9-15 were detected. The best rotational temperature
fitting of the data is 9\,K and a derived column density is
(2.7$\pm$0.3)$\times$10$^{12}$ cm$^{-2}$, which is only a factor of 4.4 below
that of its potential precursor cyclopentadiene ($c$-C$_5$H$_6$), and 1.4--1.9
times higher than that of the ethynyl derivatives of cyclopentadiene. We
searched for fulvene ($c$-C$_5$H$_4$CH$_2$), a CH$_2$ derivative of
cyclopentadiene, for which we derive a 3$\sigma$ upper limit to its column
density of (3.5$\pm$0.5)$\times$10$^{12}$ cm$^{-2}$. Upper limits were also
obtained for toluene (C$_6$H$_5$CH$_3$) and styrene (C$_6$H$_5$C$_2$H$_3$), the
methyl and vinyl derivatives of benzene. Fulvenallene and ethynyl
cyclopentadiene are likely formed in the reaction between cyclopentadiene
($c$-C$_5$H$_6$) and the ehtynyl radical (CCH). However, the bottom-up
gas-phase synthesis of cycles in TMC-1 underestimates the abundance of
cyclopentadiene by two orders of magnitude, which strengthens the need to study
all possible chemical pathways to cyclisation in cold dark cloud environments,
such as TMC-1. However, the inclusion of the reaction between C$_3$H$_3^+$ and
C$_2$H$_4$ produces a good agreement between model and observed abundances.
