C₅×#87639 #14519957

order	1960
isoclinism	isoclinic class of D₇²
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

derived, Sylow	C₇² ⋊ C₂×C₄×C₅
Hall	C₅×C₇² ⋊ C₂×C₄

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 140

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

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

maximal subgroup of	D₅×#87639, C₅×#11716115, #72243401, …
maximal normal subgroup of	D₅×#87639, C₅×#11716115, #72243401, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 54);