C₄×D₈×ΓL(1,𝔽₈) #13054968

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₄×D₈×ΓL(1,𝔽₈)
unambiguous semidirect product	(C₄×C₇×D₈)⋊C₃

Fitting, Hall	C₄×C₇×D₈ ⋊ C₃
Sylow	C₇ ⋊ C₃×C₄×D₈

268 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 111 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 — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4257);