C₂×C₃²×#483 #11770135

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

Aliases

C₂×C₃²×#483

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

1380 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 4 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4146);