ΓL(1,𝔽₈)×#535 #13060696

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product	ΓL(1,𝔽₈)×#535
unambiguous semidirect product	(C₇×#535)⋊C₃

Fitting, Hall	C₇×#535 ⋊ C₃
Sylow	C₇ ⋊ C₃×#535

668 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 4 generators on 19 points:

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

maximal subgroup of	ΓL(1,𝔽₈)×#3532, ΓL(1,𝔽₈)×#3484, AGL(1,𝔽₇)×#535, …
maximal normal subgroup of	ΓL(1,𝔽₈)×#3532, ΓL(1,𝔽₈)×#3484, AGL(1,𝔽₇)×#535, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 9985);