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C3×(C11⋊C5)⋊(D31⋊C3) #44501740

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

Aliases

direct productC3×(C11⋊C5)⋊(D31⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C3×D31⋊C3)
unambiguous semidirect product((C11⋊C5)⋊D31)⋊C32
unambiguous semidirect product(C3×(C11⋊C5)⋊D31)⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC3×C11⋊C5×C31⋊C3 ⋊ C2
HallC3×C11⋊(D31⋊C3) ⋊ C5
Hall(C11⋊C5)⋊D31 ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC31×C11⋊C5 ⋊ C2×C32
HallD341 ⋊ C32×C5
HallC3×C31⋊C3 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D31⋊C3
SylowC31 ⋊ C32×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊(D31⋊C3)
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

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 107);