Finite Group Databasebeta

← Prev (#72247901) Next (#72247903) →

C3×D3×(C31⋊C3)⋊C5 #72247902

order8370
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×D3×(C31⋊C3)⋊C5

Splittings

Fitting, socleC32×C31 ⋊ C2×C3×C5
derivedC3×C31 ⋊ C2×C32×C5
HallC32×(C31⋊C3)⋊C5 ⋊ C2
HallC3×D3×C31⋊C3 ⋊ C5
HallC32×C31⋊C3 ⋊ C2×C5
HallΓL(1,𝔽32) ⋊ C32×D3
SylowC31 ⋊ C32×C5×D3

Subgroups

subgroupG/H
center, hypercenterC3D3×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC3×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 186

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×(C31⋊C3)⋊C5, C3×D3×AGL(1,𝔽31), D3×C3⋊AGL(1,𝔽31)
maximal normal subgroup ofD32×(C31⋊C3)⋊C5, C3×D3×AGL(1,𝔽31), D3×C3⋊AGL(1,𝔽31)

GAP

Past the SmallGroups library coverage — no SmallGroups id.