C₇×C₄⋊GL(2,𝔽₃) #13057114

order	1344
isoclinism	isoclinic class of #5386
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₄⋊GL(2,𝔽₃)
unambiguous semidirect product	C₄⋊(C₇×GL(2,𝔽₃))

C₄×C₇×Q₈ ⋊ D₃

182 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 6403);