Finite Group Databasebeta

#67×C9⋊C9 #14517413

order1944
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct product#67×C9⋊C9
unambiguous semidirect product(C9×#67)⋊C9

Splittings

FittingC22×C3×C9⋊C9 ⋊ C2
SylowC3×C9⋊C9 ⋊ D4

Subgroups

subgroupG/H
center, FrattiniC2×C32C2×C32×D3
commutatorC2×C32C22×C3×C9
FittingC22×C3×C9⋊C9C2
socle, cosocleC2×C33C22×C32
prime radicalC32×#67C32
hypercenterC22×C9⋊C9D3
hypocenterC3D4×C9⋊C9
LCSG ▷ C2×C32 ▷ C3
UCSC1 ◁ C2×C32 ◁ C22×C9⋊C9

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

normal subgroups only

This group has 412 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.

Full subgroup data →

Presentation

transitive degreeμt(G) = 324

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1807);