Finite Group Databasebeta

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D9×#92262 #72254052

order8748
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productD9×#92262

Splittings

Fitting, SylowC9×C9⋊H(3,𝔽3) ⋊ C22

Subgroups

subgroupG/H
centerC3C3×D9×(C3⋊D3)⋊C3
commutator, cosocleC33×C9C22×C32
Frattini, socleC33C32×D32
FittingC9×C9⋊H(3,𝔽3)C22
prime radicalC3×D9×(C3⋊D3)⋊C3C3
hypercenterC9D9×(C3⋊D3)⋊C3
hypocenterC32×C9C22×3−1+2
LCSG ▷ C33×C9 ▷ C32×C9
UCSC1 ◁ C3 ◁ C9

1064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72254055, D9×D9⋊((C3⋊D3)⋊C3)
maximal normal subgroup of#72254055, D9×D9⋊((C3⋊D3)⋊C3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.