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C3×((C31⋊C3)⋊C5)⋊D11 #44501747

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

Aliases

direct productC3×((C31⋊C3)⋊C5)⋊D11
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C3×D11)
unambiguous semidirect product(ΓL(1,𝔽32)⋊D11)⋊C32
unambiguous semidirect product(C3×ΓL(1,𝔽32)⋊D11)⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC3×C11×(C31⋊C3)⋊C5 ⋊ C2
HallC3×C11⋊(D31⋊C3) ⋊ C5
HallΓL(1,𝔽32)⋊D11 ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C2×C32
HallC3×(C31⋊C3)⋊C5 ⋊ D11
HallD341 ⋊ C32×C5
HallC3×C31⋊C3 ⋊ C5×D11
HallΓL(1,𝔽32) ⋊ C32×D11
SylowC31 ⋊ C32×C5×D11
SylowC11 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC3((C31⋊C3)⋊C5)⋊D11
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 114);