Finite Group Databasebeta

← Prev (#11724438) Next (#11724440) →

D3×#3811 #11724439

order864
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD3×#3811

Splittings

FittingC22×C33 ⋊ C23
SylowC33 ⋊ C22×D4

Subgroups

subgroupG/H
center, FrattiniC2C2×D33
commutator, socle, cosocleC2×C33C24
FittingC22×C33C23
hypercenterC22D33
hypocenterC33C22×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

1218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#63738, #13165456, D3×#64233, …
maximal normal subgroup ofD3×#63738, #13165456, D3×#64233, …
maximal quotient ofD3×#63883, D3×#63910, #13170749, …
holomorph ofC3×Dic3, C2×C3×D3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4406);