Finite Group Databasebeta

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C3×#16811771⋊C3 #44501742

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

Aliases

direct productC3×#16811771⋊C3
unambiguous semidirect product#16811771⋊C32
unambiguous semidirect product(C3×#16811771)⋊C3

Splittings

Fitting, socleC3×C11×C31 ⋊ C2×C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC3×#13133721⋊C3 ⋊ C2
HallC3×C11×D31⋊C3 ⋊ C5
Hall#16811771 ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
Hall#13133721 ⋊ C2×C32
HallC11×D31 ⋊ C32×C5
HallC3×D31⋊C3 ⋊ C11⋊C5
HallC3×C31⋊C3 ⋊ C2×C11⋊C5
HallD31 ⋊ C32×C11⋊C5
SylowC31 ⋊ C2×C32×C11⋊C5
SylowC11 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC3#16811771⋊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

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 109);