C₃×#89428 #13055094

order	1344
isoclinism	isoclinic class of #89428
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₇ ⋊ #395
Sylow	C₇ ⋊ C₃×#395

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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)(12,14)(15,16,17,18);(11,12)(13,14)(19,21,22,26)(20,23,24,25);(5,6)(7,8)(9,10)(16,18)(19,20,22,24)(21,25,26,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4383);