C₅×#983 #91942

order	480
automorphism	Aut(G) = C₂²×C₄×S₄ (order 384) · Inn(G) = C₂×S₄ · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×Q₈ ⋊ D₃

	subgroup	G/H
center, socle	C₂×C₅	C₂×S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂	C₂×C₅×S₄
Fitting	C₂×C₅×Q₈	D₃
hypercenter	C₂²×C₅	S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₅

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1018);