C₇×#4467 #13051252

order	1344
isoclinism	isoclinic class of #4451
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ #328
Sylow	C₃ ⋊ C₇×#328

160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 336

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 541);