Finite Group Databasebeta

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C3×C31⋊C3×C121 #46798246

order33759
automorphism?
homologyAbelianization (H1) = C32×C121 · Schur multiplier (H2) = C3

Aliases

direct productC3×C31⋊C3×C121
unambiguous semidirect productC31⋊(C32×C121)
unambiguous semidirect product(C3×C31)⋊(C3×C121)
unambiguous semidirect product(C31×C121)⋊C32
unambiguous semidirect product(C3×C31×C121)⋊C3

Splittings

FittingC3×C31×C121 ⋊ C3
derived, SylowC31 ⋊ C32×C121
HallC31×C121 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C121C31⋊C3
commutator, hypocenterC31C32×C121
FrattiniC11C3×C11×C31⋊C3
FittingC3×C31×C121C3
socleC3×C11×C31C3×C11
prime radicalC3×C11×C31⋊C3C11
cosocleC11×C31C32×C11
LCSG ▷ C31
UCSC1 ◁ C3×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11253

Conjugacy classes & character table

4719 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33759, 4);