C₇×#4925 #13055960

order	1344
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₇ ⋊ #431
Sylow	C₃ ⋊ C₇×#431

236 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:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5249);