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C3×C31⋊C3×AGL(1,𝔽11) #44501741

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C31⋊C3×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C31⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C31⋊C3)
unambiguous semidirect product(C3×D11)⋊(C5×C31⋊C3)
unambiguous semidirect product(C31×AGL(1,𝔽11))⋊C32
unambiguous semidirect product(C3×C31×AGL(1,𝔽11))⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC3×C11⋊C5×C31⋊C3 ⋊ C2
HallC3×D11×C31⋊C3 ⋊ C5
HallC31×AGL(1,𝔽11) ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC31×C11⋊C5 ⋊ C2×C32
HallD11×C31 ⋊ C32×C5
HallC11⋊C5 ⋊ C2×C3×C31⋊C3
SylowC31 ⋊ C32×AGL(1,𝔽11)
HallD11 ⋊ C3×C5×C31⋊C3
SylowC11 ⋊ C2×C3×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C31⋊C3×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 108);