C₇×#4451 #13051233

order	1344
isoclinism	isoclinic class of #4451
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂²

Aliases

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

normal subgroups only

This group has 180 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)(12,15,16,17)(14,18)(20,23,24,25);(9,10)(11,12)(13,17)(14,16)(15,18)(19,20)(21,23)(22,24)(25,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 522);