C₂×C₃×D₅⋊C₈ #91971

order	480
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₃×D₅⋊C₈
unambiguous semidirect product	D₅⋊(C₂×C₃×C₈)

derived, Sylow	C₅ ⋊ C₂²×C₃×C₈
Hall	C₃×C₅ ⋊ C₂²×C₈

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1047);