C₃×#89324 #13051189

order	1344
isoclinism	isoclinic class of #1141
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₇ ⋊ #340
Sylow	C₇ ⋊ C₃×#340

228 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 478);