C₃×A₅ #4374

order	180
isoclinism	isoclinic class of A₅
automorphism	Aut(G) = C₂×S₅ (order 240) · Inn(G) = A₅ · Out(G) = C₂²
holomorph	G ⋊ Aut(G) = D₃×#72219548
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₂

Aliases

general linear	GL(2,𝔽₄)
direct product	C₃×A₅

21 conjugacy classes of subgroups.

minimal degree	μ(G) = 8
transitive degree	μ_t(G) = 15

A minimal faithful permutation representation — 2 generators on 8 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(180, 19);