Finite Group Databasebeta

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C9×C31×D55 #44501653

order30690
automorphism?
homologyAbelianization (H1) = C2×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×D55
unambiguous semidirect productC5⋊(C9×D11×C31)
unambiguous semidirect productC11⋊(C9×D5×C31)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC5×C11 ⋊ C2×C9×C31
HallC9×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ C2×C9
HallC5×C9×C31 ⋊ D11
HallC5×C9×C11 ⋊ C2×C31
HallC11×C31 ⋊ C9×D5
HallC5×C31 ⋊ C9×D11
HallC9×C11 ⋊ D5×C31
HallC5×C9 ⋊ D11×C31
SylowC11 ⋊ C9×D5×C31
SylowC5 ⋊ C9×D11×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31D55
commutator, hypocenterC5×C11C2×C9×C31
FrattiniC3C3×C31×D55
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31C2×C3
prime radicalC3×C31×D55C3
cosocleC3×C5×C11C2×C3×C31
LCSG ▷ C5×C11
UCSC1 ◁ C9×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

8091 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 20);