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C31×C9⋊AGL(1,𝔽11) #44501694

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

Aliases

direct productC31×C9⋊AGL(1,𝔽11)
unambiguous semidirect productC9⋊(C31×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D9×C31)
unambiguous semidirect productD99⋊(C5×C31)

Splittings

Fitting, HallC9×C11×C31 ⋊ C2×C5
derived, HallC9×C11 ⋊ C2×C5×C31
HallC9×C31×C11⋊C5 ⋊ C2
HallC31×D99 ⋊ C5
HallC31×C11⋊C5 ⋊ D9
HallC9×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C5×D9
HallC9×C31 ⋊ AGL(1,𝔽11)
HallD99 ⋊ C5×C31
HallC11⋊C5 ⋊ D9×C31
SylowC11 ⋊ C5×D9×C31
SylowC9 ⋊ C31×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC31C9⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC9×C11C2×C5×C31
FrattiniC3C31×C3⋊AGL(1,𝔽11)
FittingC9×C11×C31C2×C5
socleC3×C11×C31C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

1209 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 61);