Finite Group Databasebeta

D9×#23900 #72268884

order4608
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C212

Aliases

direct productD9×#23900

Splittings

FittingC9×#23900 ⋊ C2
SylowC9 ⋊ C2×#23900

Subgroups

subgroupG/H
centerC22C2×D9×#120
commutator, cosocleC24×C9C25
FrattiniC24×C3C24×D3
FittingC9×#23900C2
socleC22×C3C2×D3×#120
hypercenter#23900D9
hypocenterC9C2×#23900
LCSG ▷ C24×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C25 ◁ #23900

44976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.