Finite Group Databasebeta

C2×C4×D9×C3⋊D3 #72275944

order2592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×C4×D9×C3⋊D3

Splittings

FittingC2×C32×C4×C9 ⋊ C22
derived, SylowC32×C9 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4D9×C3⋊D3
commutator, hypocenterC32×C9C23×C4
FrattiniC2×C3C22×D3×C3⋊D3
FittingC2×C32×C4×C9C22
socleC22×C33C22×D3
prime radicalC22×D9×C3⋊D3C2
cosocleC2×C32×C9C24
LCSG ▷ C32×C9
UCSC1 ◁ C2×C4

2556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×D4×D9×C3⋊D3
maximal normal subgroup ofC2×D4×D9×C3⋊D3

GAP

Past the SmallGroups library coverage — no SmallGroups id.