C₂×C₅×#41⋊C₃ #92054

order	480
isoclinism	isoclinic class of SL(2,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×#41⋊C₃
unambiguous semidirect product	(C₂×#41)⋊(C₃×C₅)
unambiguous semidirect product	(C₂×C₅×#41)⋊C₃

Fitting, Hall	C₂×C₅×#41 ⋊ C₃
Sylow	C₂×#41 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃×C₅
Frattini	C₂	C₂²×C₅×A₄
Fitting	C₂×C₅×#41	C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₄×C₅

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2)(3,4,5,6,7)(8,9,12,15)(10,14,18,21,11,20,17,23,16,13,19,22);(1,2)(8,16,12,18)(9,20,15,22)(10,19,17,11)(13,23,21,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1130);