A₅⋊Q₈ #91869

order	480
automorphism	Aut(G) = D₄×S₅ (order 960) · Inn(G) = C₂×S₅ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

A₅⋊Q₈

	subgroup	G/H
center, Frattini	C₂	C₂×S₅
commutator, socle, prime radical, cosocle	C₂×A₅	C₂²
Fitting, hypercenter	C₄	S₅
hypocenter	A₅	Q₈
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 945);