Finite Group Databasebeta

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C2×C3×#13133721⋊C3 #44501774

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

Aliases

direct productC2×C3×#13133721⋊C3
unambiguous semidirect product(C2×#13133721)⋊C32
unambiguous semidirect product(C2×C3×#13133721)⋊C3

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C3×C5
derived, HallC11×C31 ⋊ C2×C32×C5
HallC2×C3×C11×C31⋊C3 ⋊ C5
HallC2×#13133721 ⋊ C32
HallC3×C11×C31⋊C3 ⋊ C2×C5
Hall#13133721 ⋊ C2×C32
HallC2×C11×C31 ⋊ C32×C5
HallC2×C3×C31⋊C3 ⋊ C11⋊C5
HallC3×C31⋊C3 ⋊ C2×C11⋊C5
HallC2×C31 ⋊ C32×C11⋊C5
SylowC31 ⋊ C2×C32×C11⋊C5
HallC2×C11 ⋊ C3×(C31⋊C3)⋊C5
SylowC11 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#13133721⋊C3
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 141);