C₅×#985 #91944

order	480
isoclinism	isoclinic class of #226
automorphism	Aut(G) = C₂²×C₄×S₄ (order 384) · Inn(G) = S₄ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₄×C₅	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂	C₂×C₅×S₄
Fitting	C₅×#41	D₃
socle	C₂×C₅	C₂×S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₄×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1020);