C₅×C₄⋊(C₇⋊D₇) #14519994

order	1960
isoclinism	isoclinic class of #87648
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₅×C₄⋊(C₇⋊D₇)
unambiguous semidirect product	C₄⋊(C₅×C₇⋊D₇)

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 980

A minimal faithful permutation representation — 3 generators on 23 points:

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

505 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 91);