C₃²×#3306 #11770355

order	1152
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄ ◁ G

1326 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 4 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4366);