C₅²×C₇⋊C₈ #13063752

order	1400
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₅²×C₈ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₇⋊C₈
unambiguous semidirect product	C₇⋊(C₅²×C₈)

derived, Sylow	C₇ ⋊ C₅²×C₈
Hall	C₅²×C₇ ⋊ C₈

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1400

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5)(12,13)(14,15)(16,17)(18,19,20,22,21,23,24,25);(6,7,8,9,10)(11,12,14,16,17,15,13)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 41);