Finite Group Databasebeta

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C2×D3×#13133724 #35205809

order20460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×#13133724
unambiguous semidirect productC3⋊(C22×#13133724)
unambiguous semidirect product(C2×C3)⋊(C2×#13133724)

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C2×C5
derived, HallC3×C11×C31 ⋊ C22×C5
HallC3×#13133724 ⋊ C22
HallC2×D3×C11×C31 ⋊ C5
HallC2×D3×C31 ⋊ C11⋊C5
HallC11×C31 ⋊ C2×C5×D3
HallC2×D3×C11 ⋊ ΓL(1,𝔽32)
HallC3×C31 ⋊ C22×C11⋊C5
HallC3×C11 ⋊ C22×ΓL(1,𝔽32)
SylowC31 ⋊ C2×D3×C11⋊C5
SylowC11 ⋊ C2×D3×ΓL(1,𝔽32)
SylowC3 ⋊ C22×#13133724

Subgroups

subgroupG/H
center, hypercenterC2D3×#13133724
commutator, cosocle, hypocenterC3×C11×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 229);