C₇×D₄⋊(C₃⋊C₈) #13051316

order	1344
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₇×D₄⋊(C₃⋊C₈)
unambiguous semidirect product	D₄⋊(C₇×C₃⋊C₈)

Hall	C₃×C₇ ⋊ D₄⋊C₈
Sylow	C₃ ⋊ C₇×D₄⋊C₈

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

normal subgroups only

This group has 164 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) = 672

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

(1,2,3,4,5,6,7)(8,9,10)(20,23)(21,26)(24,25);(9,10)(11,12,13,15,14,16,17,18)(19,20)(21,23)(22,25)(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, 605);