C₃²×#1627 #11768676

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

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃²
prime radical	C₃²×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ G

750 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)(7,8)(9,11)(10,13)(12,14)(16,20)(17,21)(18,22);(4,5,6)(8,11)(9,14)(12,13)(15,16,19,17)(18,21,22,20);(15,17,19,16)(18,20,22,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2687);