C₂×C₃²×#462 #11770082

order	1152
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₂×C₃²×#462

	subgroup	G/H
center, socle, prime radical	C₂³×C₃²	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ C₂×C₃²×C₄² ◁ G

1440 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2)(23,24,25);(4,6)(7,8,11,14)(9,15,17,22)(10,18,20,13)(12,19,21,16)(26,27,28);(3,4,5,6);(7,9,11,17)(8,12,14,21)(10,19,20,16)(13,22,18,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4093);