C₅×#5997⋊C₂ #14520024

order	1960
isoclinism	isoclinic class of #5997⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×#5997⋊C₂
unambiguous semidirect product	#5997⋊(C₂×C₅)
unambiguous semidirect product	D₇²⋊(C₂×C₅)

Fitting, socle, Hall	C₅×C₇² ⋊ D₄
Sylow	C₇² ⋊ C₅×D₄

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 70

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 121);