C₅²×D₂₈ #13063799

order	1400
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅²×D₂₈
unambiguous semidirect product	C₄⋊(C₅²×D₇)

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 700

A minimal faithful permutation representation — 2 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 88);