D₅×#11713200 #72243463

order	7680
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

Fitting	C₅×#2846 ⋊ C₂×D₃
Sylow	C₅ ⋊ C₂×#11713200

At least 11304 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 60

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

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

maximal subgroup of	AGL(1,𝔽₅)×#11713200
maximal normal subgroup of	AGL(1,𝔽₅)×#11713200

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,3)(4,5)(11,17,15)(12,13,16), (1,2,4,5,3)(7,9), (12,16)(14,17), (6,7)(8,9)(10,11)(12,14)(13,15)(16,17));