ΓL(1,𝔽₈)×#547 #13060708

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	ΓL(1,𝔽₈)×#547
unambiguous semidirect product	(C₇×#547)⋊C₃

Fitting, Hall	C₇×#547 ⋊ C₃
Sylow	C₇ ⋊ C₃×#547

584 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 9997);