ΓL(1,𝔽₈)×#483 #13055014

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	ΓL(1,𝔽₈)×#483
unambiguous semidirect product	(C₇×#483)⋊C₃

Fitting, Hall	C₇×#483 ⋊ C₃
Sylow	C₇ ⋊ C₃×#483

208 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4303);