C₇×#4977 #13056006

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Hall	C₃×C₇ ⋊ #382
Sylow	C₃ ⋊ C₇×#382

308 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 158 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:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5295);