C₃²×#1705 #11768754

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₃×C₈

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃²
prime radical	C₃²×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ G

642 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)(16,19)(17,21)(20,22);(4,5,6)(7,8,9,11,10,12,13,14);(15,16,17,19,18,20,21,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 2765);