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C31×C3⋊(C3⋊AGL(1,𝔽11)) #44501823

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC31×C3⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C31×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊D3×C31)
unambiguous semidirect product(C3⋊D33)⋊(C5×C31)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C31
HallC32×C31×C11⋊C5 ⋊ C2
HallC31×C3⋊D33 ⋊ C5
HallC31×C11⋊C5 ⋊ C3⋊D3
HallC32×C11⋊C5 ⋊ C2×C31
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ AGL(1,𝔽11)
HallC3⋊D33 ⋊ C5×C31
HallC11⋊C5 ⋊ C3⋊D3×C31
SylowC11 ⋊ C5×C3⋊D3×C31
SylowC32 ⋊ C31×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC31C3⋊(C3⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC32×C11C2×C5×C31
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C31

96 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, 190);