C₃²×#1651 #11768700

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃²
prime radical	C₂×C₃²×D₄	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ G

702 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2711);