C₂²×D₅⋊C₈ #66249

order	320
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×D₅⋊C₈
unambiguous semidirect product	D₅⋊(C₂²×C₈)

C₅ ⋊ C₂³×C₈

338 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1587);