C₂×#5997 #87660

order	392
isoclinism	isoclinic class of #5997
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₇

Aliases

Fitting, socle	C₂×C₇² ⋊ C₄
derived, Sylow	C₇² ⋊ C₂×C₄

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 28

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 40);