C₃×#89750 #13055405

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₇ ⋊ #387
Sylow	C₇ ⋊ C₃×#387

308 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1344

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(21,25)(23,26);(16,18)(19,21,22,25)(20,23,24,26);(5,6)(7,8)(9,10)(15,16)(17,18)(19,20,22,24)(21,23,25,26)

264 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4694);