Finite Group Databasebeta

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C9×(C11⋊C5)⋊D31 #44501676

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

Aliases

direct productC9×(C11⋊C5)⋊D31
unambiguous semidirect product(C11⋊C5)⋊(C9×D31)

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C2×C5×C9
HallC9×C31×C11⋊C5 ⋊ C2
HallC9×D341 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C9
HallD341 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ D31
HallC9×C31 ⋊ AGL(1,𝔽11)
HallC9×C11 ⋊ C5×D31
HallC11⋊C5 ⋊ C9×D31
SylowC31 ⋊ C9×AGL(1,𝔽11)
SylowC11 ⋊ C5×C9×D31

Subgroups

subgroupG/H
center, hypercenterC9(C11⋊C5)⋊D31
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C3×(C11⋊C5)⋊D31
FittingC9×C11×C31C2×C5
socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×(C11⋊C5)⋊D31C3
LCSG ▷ C11×C31
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 43);