C₇²×C₂²⋊D₅ #14520001

order	1960
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇² · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₇²×C₂²⋊D₅
unambiguous semidirect product	C₂²⋊(C₇²×D₅)

160 conjugacy classes of subgroups.

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

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 98);