C₃×#89697 #13055358

order	1344
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₇ ⋊ #431
Sylow	C₇ ⋊ C₃×#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)(4,5,7,9,10,8,6)(20,24)(23,26);(19,21,22,25)(20,23,24,26);(5,6)(7,8)(9,10)(11,12,13,15,14,16,17,18)(19,20)(21,23)(22,24)(25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4647);