Finite Group Databasebeta

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D9×#13133722 #44501685

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

Aliases

direct productD9×#13133722
unambiguous semidirect productC9⋊(C2×#13133722)

Splittings

Fitting, derived, HallC9×C11×C31 ⋊ C2×C5
HallC9×#13133722 ⋊ C2
HallC11×D9×C31 ⋊ C5
HallD9×C31 ⋊ C11⋊C5
HallC11×C31 ⋊ C5×D9
HallC9×C31 ⋊ C2×C11⋊C5
HallC11×D9 ⋊ ΓL(1,𝔽32)
HallC9×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ D9×C11⋊C5
SylowC11 ⋊ D9×ΓL(1,𝔽32)
SylowC9 ⋊ C2×#13133722

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C11×C31C2×C5
FrattiniC3D3×#13133722
socleC3×C11×C31C5×D3
LCSG ▷ C9×C11×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 52);