C₇×D₂₈ #87645

order	392
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₂₈
unambiguous semidirect product	C₄⋊(C₇×D₇)

Fitting	C₄×C₇² ⋊ C₂
Sylow	C₇² ⋊ D₄

41 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 56

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 25);