Finite Group Databasebeta

← Prev (#72277019) Next (#72277021) →

C2×3−1+2×C13⋊C3 #72277020

order2106
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C32

Aliases

direct productC2×3−1+2×C13⋊C3

Splittings

FittingC2×C13×3−1+2 ⋊ C3
HallC2×C13 ⋊ C3×3−1+2
SylowC13 ⋊ C2×C3×3−1+2

Subgroups

subgroupG/H
centerC2×C3C32×C13⋊C3
commutator, cosocleC3×C13C2×C33
FrattiniC3C2×C32×C13⋊C3
FittingC2×C13×3−1+2C3
socleC2×C3×C13C33
prime radicalC2×C32×C13⋊C3C3
hypercenterC2×3−1+2C13⋊C3
hypocenterC13C2×C3×3−1+2
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 234

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×3−1+2×D13⋊C3, C2×C13⋊C3×AGL(1,ℤ/9), C2×#72228951
maximal normal subgroup ofC2×3−1+2×D13⋊C3, C2×C13⋊C3×AGL(1,ℤ/9), C2×#72228951

GAP

Past the SmallGroups library coverage — no SmallGroups id.