C₂⁴×C₃²×D₄ #11770637

order	1152
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₃² · Schur multiplier (H₂) = C₂¹⁵×C₃

Aliases

direct product	C₂⁴×C₃²×D₄
unambiguous semidirect product	C₄⋊(C₂⁵×C₃²)

	subgroup	G/H
center, socle	C₂⁵×C₃²	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₃²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₃² ◁ G

31656 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 6 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4648);