Finite Group Databasebeta

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C9×C31×AGL(1,𝔽11) #44501670

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C9×C31)
unambiguous semidirect product(C11⋊C5)⋊(C2×C9×C31)
unambiguous semidirect product(C9×D11)⋊(C5×C31)

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C9×C31
HallC9×C31×C11⋊C5 ⋊ C2
HallC9×D11×C31 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×C9
HallD11×C31 ⋊ C5×C9
HallC9×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C2×C5×C9
HallC9×D11 ⋊ C5×C31
HallC9×C11 ⋊ C2×C5×C31
HallC11⋊C5 ⋊ C2×C9×C31
HallD11 ⋊ C5×C9×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C9×C31
FrattiniC3C3×C31×AGL(1,𝔽11)
FittingC9×C11×C31C2×C5
socleC3×C11×C31C2×C3×C5
prime radicalC3×C31×AGL(1,𝔽11)C3
cosocleC3×C11C2×C3×C5×C31
LCSG ▷ C11
UCSC1 ◁ C9×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 37);