Finite Group Databasebeta

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C9×#92262 #72243687

order4374
automorphism?
homologyAbelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC9×#92262

Splittings

Fitting, SylowC9×C9⋊H(3,𝔽3) ⋊ C2

Subgroups

subgroupG/H
centerC3×C9C3×(C3⋊D3)⋊C3
commutatorC33C2×C32×C9
Frattini, socleC33C33×D3
FittingC9×C9⋊H(3,𝔽3)C2
prime radicalC32×(C3⋊D3)⋊C3C32
cosocleC34C2×C33
hypercenterC92(C3⋊D3)⋊C3
hypocenterC32C2×C9×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C3×C9 ◁ C92

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 486

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72243705, #72243962, C9×D9⋊((C3⋊D3)⋊C3), …
maximal normal subgroup of#72243705, #72243962, C9×D9⋊((C3⋊D3)⋊C3), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.