C₇×#4535 #13051317

order	1344
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ Q₈⋊C₈
Sylow	C₃ ⋊ C₇×Q₈⋊C₈

140 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 78 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 — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 606);