Finite Group Databasebeta

C3×#23779831 #44525003

order30861
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×#23779831

Splittings

FittingC32×C9×C127 ⋊ C3
SylowC127 ⋊ C3×C32⋊C9

Subgroups

subgroupG/H
centerC33C3×C127⋊C3
commutatorC3×C127C32×C9
FrattiniC32C32×C127⋊C3
FittingC32×C9×C127C3
socleC33×C127C32
prime radicalC33×C127⋊C3C3
cosocleC32×C127C33
hypercenterC32×C9C127⋊C3
hypocenterC127C3×C32⋊C9
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C33 ◁ C32×C9

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10287

Conjugacy classes & character table

3501 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 157);