C₂×ΓL(1,𝔽₈)×M₃₂ #13055034

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×ΓL(1,𝔽₈)×M₃₂
unambiguous semidirect product	(C₂×C₇×M₃₂)⋊C₃

Fitting, Hall	C₂×C₇×M₃₂ ⋊ C₃
Sylow	C₇ ⋊ C₂×C₃×M₃₂

180 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2)(20,21,22)(23,25,24);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21,23,22,24,25);(4,12)(6,14)(8,16)(10,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4323);