C₇×#4981 #13056018

order	1344
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ #398
Sylow	C₃ ⋊ C₇×#398

300 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 126 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)(12,14)(19,21,22,25)(20,23,24,26);(15,16,17,18)(21,25)(23,26);(9,10)(11,12)(13,14)(16,18)(19,20,22,24)(21,23,25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5307);