Finite Group Databasebeta

C3×C9×C373⋊C3 #44475088

order30213
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC3×C9×C373⋊C3

Splittings

FittingC3×C9×C373 ⋊ C3
derived, SylowC373 ⋊ C32×C9

Subgroups

subgroupG/H
center, hypercenterC3×C9C373⋊C3
commutator, hypocenterC373C32×C9
FrattiniC3C32×C373⋊C3
FittingC3×C9×C373C3
socleC32×C373C32
prime radicalC32×C373⋊C3C3
cosocleC3×C373C33
LCSG ▷ C373
UCSC1 ◁ C3×C9

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10071

Conjugacy classes & character table

3429 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30213, 38);