C₃×#89420 #13055082

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂×C₄²

Aliases

Hall	C₃×C₇ ⋊ #376
Sylow	C₇ ⋊ C₃×#376

356 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4371);