Q₈×A₆ #72228166

order	2880
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

Q₈×A₆

	subgroup	G/H
center, Frattini, cosocle	C₂	C₂²×A₆
commutator, socle, prime radical	C₂×A₆	C₂²
Fitting, hypercenter	Q₈	A₆
hypocenter	A₆	Q₈
LCS	G ▷ C₂×A₆ ▷ A₆
UCS	C₁ ◁ C₂ ◁ Q₈

244 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 14 points:

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,4,2,6)(3,7,5,8)(9,12,14,11,10), (1,3,2,5)(4,8,6,7)(9,14,10,12,13));