Finite Group Databasebeta

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C31×C22⋊(C31⋊C9) #46829327

order34596
automorphism?
homologyAbelianization (H1) = C9×C31 · Schur multiplier (H2) = C2

Aliases

direct productC31×C22⋊(C31⋊C9)
unambiguous semidirect productC22⋊(C31×C31⋊C9)
unambiguous semidirect productC31⋊(C31×C22⋊C9)

Splittings

derivedC22×C31 ⋊ C9×C31
HallC22×C312 ⋊ C9
SylowC312 ⋊ C22⋊C9
SylowC22 ⋊ C31×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C31C22⋊(C31⋊C3)
commutator, hypocenterC22×C31C9×C31
FrattiniC3C31×C22⋊(C31⋊C3)
Fitting, socle, prime radicalC22×C3×C312C3
cosocleC22×C3×C31C3×C31
LCSG ▷ C22×C31
UCSC1 ◁ C3×C31

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 558

Conjugacy classes & character table

4092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 87);