Finite Group Databasebeta

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AGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3 #72247474

order19440
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3

Splittings

Fitting, HallC5×#6891 ⋊ C22×C4
derivedC5×C32⋊C9 ⋊ C22×C3×C4
Sylow#6891 ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C4×(((C3⋊D3)⋊C9)⋊C2)⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC5×C32⋊C9C22×C3×C4
FrattiniC32C3×D32×AGL(1,𝔽5)
FittingC5×#6891C22×C4
socleC32×C5C3×C4×D32
prime radicalD5×(((C3⋊D3)⋊C9)⋊C2)⋊C3C2
cosocleD5×C32⋊C9C23×C3
LCSG ▷ C5×C32⋊C9
UCSC1

1760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.