Finite Group Databasebeta

D32×C27⋊C3 #72243562

order2916
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2

Aliases

direct productD32×C27⋊C3

Splittings

Fitting, SylowC32×C27⋊C3 ⋊ C22

Subgroups

subgroupG/H
center, FrattiniC9C32×D32
commutator, socleC33C22×C3×C9
FittingC32×C27⋊C3C22
prime radicalC32×D32C9
cosocleC32×C9C22×C32
hypercenterC27⋊C3D32
hypocenterC32C22×C27⋊C3
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C9 ◁ C27⋊C3

472 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 108

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD32×D27⋊C3, D32×#6875
maximal normal subgroup ofD32×D27⋊C3, D32×#6875

GAP

Past the SmallGroups library coverage — no SmallGroups id.