#120⋊C₉ #63425

order	288
isoclinism	isoclinic class of #120⋊C₃
automorphism	Aut(G) = C₃×#4625⋊C₂ (order 1152) · Inn(G) = #120⋊C₃ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂²

Aliases

derived	C₂⁴ ⋊ C₂×C₉
Sylow	#120 ⋊ C₉

62 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 17 points:

(1,5,9,3,8,4,6,2,7)(10,11)(12,15,16,14,13,17);(11,17)(14,15)

Polycyclic presentation:

2,3^2,2^4|b^3=c,d^a=df,e^a=eg,d^b=e,e^b=de,f^b=g,g^b=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 73);