Finite Group Databasebeta

C2×C9×#809 #13142581

order1728
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C24

Aliases

direct productC2×C9×#809

Splittings

FittingC2×C3×C9×C4⋊C4 ⋊ C2
SylowC3×C9 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23×C9#67
commutatorC3×C4C22×C4×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C9×C4⋊C4C2
socleC23×C32C3×D4
prime radicalC22×C3×D12C2×C3
cosocleC2×C32×C4C23×C3
hypercenterC2×C9×C4⋊C4D3
hypocenterC3C2×C9×#102
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C9 ◁ C22×C4×C9 ◁ C2×C9×C4⋊C4

698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8644);