C₂×D₅×SL(2,𝔽₃) #91963

order	480
isoclinism	isoclinic class of C₅⋊(#41⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×SL(2,𝔽₃)
unambiguous semidirect product	C₅⋊(C₂²×SL(2,𝔽₃))
unambiguous semidirect product	(C₂×C₅)⋊(C₂×SL(2,𝔽₃))
unambiguous semidirect product	(C₂×Q₈×D₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₂²	D₅×A₄
commutator, cosocle, hypocenter	C₅×Q₈	C₂²×C₃
Frattini	C₂	C₂×D₅×A₄
Fitting	C₂×C₅×Q₈	C₂×C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₂²

122 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 15 points:

(1,2)(4,5)(6,7)(9,10,12)(13,15,14);(1,2)(3,4,6,7,5)(8,12,11,14)(9,15,13,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1039);