Finite Group Databasebeta

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C5×C31×D99 #44501657

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31×D99
unambiguous semidirect productC9⋊(C5×D11×C31)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC9×C11 ⋊ C2×C5×C31
HallC9×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ D9
HallC5×C9×C31 ⋊ D11
HallC5×C9×C11 ⋊ C2×C31
HallC11×C31 ⋊ C5×D9
HallC9×C31 ⋊ C5×D11
HallC5×C11 ⋊ D9×C31
HallC5×C9 ⋊ D11×C31
SylowC11 ⋊ C5×D9×C31
SylowC9 ⋊ C5×D11×C31

Subgroups

subgroupG/H
center, hypercenterC5×C31D99
commutator, cosocle, hypocenterC9×C11C2×C5×C31
FrattiniC3C5×C31×D33
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31D3
LCSG ▷ C9×C11
UCSC1 ◁ C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7905 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 24);