C₇×#4511 #13051293

order	1344
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₇ ⋊ #364
Sylow	C₃ ⋊ C₇×#364

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 336

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 582);