C₃×#89698 #13055359

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

Aliases

Hall	C₃×C₇ ⋊ #432
Sylow	C₇ ⋊ C₃×#432

220 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 672

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4648);