Finite Group Databasebeta

C2×C9×#611⋊C3 #72276156

order3888
automorphism?
homologyAbelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C9×#611⋊C3

Splittings

FittingC23×C9×3−1+2 ⋊ C2
SylowC9×3−1+2 ⋊ C2×D4

Subgroups

subgroupG/H
centerC22×C9C2×AGL(1,ℤ/9)
commutatorC2×C9C23×C3×C9
FrattiniC2×C32C22×C32×D3
FittingC23×C9×3−1+2C2
socleC22×C32C2×C32×D3
prime radicalC2×C3×#611⋊C3C3
cosocleC2×C3×C9C23×C32
hypercenterC23×C9AGL(1,ℤ/9)
hypocenterC9C2×C3×D4×C9
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C9 ◁ C23×C9

1162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.