C₇×#4936 #13055970

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 174 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 174 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)(15,17,18,16)(20,24)(23,26);(15,16,18,17)(19,21,22,25)(20,23,24,26);(9,10)(11,12,13,14)(16,17)(19,20)(21,23)(22,24)(25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5259);