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C31×D495 #44501661

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

Aliases

direct productC31×D495
unambiguous semidirect productC5⋊(C31×D99)
unambiguous semidirect productC9⋊(C31×D55)
unambiguous semidirect productC11⋊(C31×D45)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC5×C9×C11 ⋊ C2×C31
HallC9×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ D9
HallC5×C9×C31 ⋊ D11
HallC11×C31 ⋊ D45
HallC9×C31 ⋊ D55
HallC5×C31 ⋊ D99
HallC9×C11 ⋊ D5×C31
HallC5×C11 ⋊ D9×C31
HallC5×C9 ⋊ D11×C31
SylowC11 ⋊ C31×D45
SylowC9 ⋊ C31×D55
SylowC5 ⋊ C31×D99

Subgroups

subgroupG/H
center, hypercenterC31D495
commutator, cosocle, hypocenterC5×C9×C11C2×C31
FrattiniC3C31×D165
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31D3
LCSG ▷ C5×C9×C11
UCSC1 ◁ C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7719 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 28);