C₃×#89491 #13055152

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #432
Sylow	C₇ ⋊ C₃×#432

220 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 672

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4441);