Finite Group Databasebeta

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C5×D11×C31⋊C9 #44501706

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D11×C31⋊C9
unambiguous semidirect product(C5×D11×C31)⋊C9

Splittings

derived, HallC11×C31 ⋊ C2×C5×C9
HallC5×C11×C31⋊C9 ⋊ C2
HallC5×D11×C31 ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
HallC5×C11×C31 ⋊ C2×C9
HallD11×C31 ⋊ C5×C9
HallC5×C31 ⋊ C9×D11
HallC5×C11 ⋊ C2×C31⋊C9
SylowC31 ⋊ C5×C9×D11
SylowC11 ⋊ C2×C5×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×C31⋊C3
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C5×D11×C31⋊C3
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×C5×D11×C31C3
cosocleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 73);