C₃²×#3498 #11770547

order	1152
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃² · Schur multiplier (H₂) = C₂⁹×C₃

Aliases

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

5244 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 5 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4558);