C₉×#1996 #11766717

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

	subgroup	G/H
center	C₂²×C₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₉
Frattini, prime radical, cosocle	C₂⁴×C₃	C₂³×C₃
socle	C₂²×C₃	C₂×C₃×C₂²⋊C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

486 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7,8,9)(10,11)(12,16)(13,14)(15,17)(18,19)(20,22,24,25)(21,23);(11,14)(15,16)(18,20)(19,22,23,25)(21,24);(10,12,13,17)(11,15,14,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 728);