C₂⁴×D₃ #1023

order	96
isoclinism	isoclinic class of D₃
automorphism	Aut(G) order 1935360
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product	C₂⁴×D₃
unambiguous semidirect product	C₃⋊C₂⁵
unambiguous semidirect product	(C₂×C₃)⋊C₂⁴

Fitting, socle	C₂⁴×C₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	D₃
commutator, cosocle, hypocenter	C₃	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴

748 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 5 generators on 11 points:

(1,2)(3,4)(5,6)(7,8)(10,11);(7,8)(9,10,11);(5,6);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 230);