Finite Group Databasebeta

C3×#22579488 #40996802

order26487
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×#22579488

Splittings

SylowC109 ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
centerC33C3×C109⋊C3
commutatorC3×C109C32×C9
FrattiniC32C32×C109⋊C3
FittingC32×C9×C109C3
socle, prime radicalC33×C109C32
cosocleC32×C109C33
hypercenterC32×C9C109⋊C3
hypocenterC109C3×C9⋊C9
LCSG ▷ C3×C109 ▷ C109
UCSC1 ◁ C33 ◁ C32×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26487

Conjugacy classes & character table

3015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26487, 160);