Finite Group Databasebeta

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C22×C3×#88907 #72244741

order5184
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C25×C32

Aliases

direct productC22×C3×#88907

Splittings

SylowC26 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC22×C32C3×C22⋊A4
commutator, cosocleC24×C3C22×C33
FrattiniC3C22×C32×C22⋊A4
Fitting, prime radicalC26×C33C3
socleC26×C32C32
hypercenterC22×C33C22⋊A4
hypocenterC24C22×C3×3−1+2
LCSG ▷ C24×C3 ▷ C24
UCSC1 ◁ C22×C32 ◁ C22×C33

27370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#72220143, C22×#72220148
maximal normal subgroup ofC22×#72220143, C22×#72220148

GAP

Past the SmallGroups library coverage — no SmallGroups id.