C₂×C₇⋊Dic₇ #87651

order	392
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₇⋊Dic₇
unambiguous semidirect product	(C₂×C₇)⋊Dic₇

C₇² ⋊ C₂×C₄

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 392

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 31);