ΓL(1,𝔽₈)×#388 #13054919

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

Aliases

direct product	ΓL(1,𝔽₈)×#388
unambiguous semidirect product	(C₇×#388)⋊C₃

Fitting, Hall	C₇×#388 ⋊ C₃
Sylow	C₇ ⋊ C₃×#388

380 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4208);