Finite Group Databasebeta

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C2×C3×D1749 #35230625

order20988
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D1749
unambiguous semidirect product(C2×C3)⋊(C3×D583)
unambiguous semidirect product(C2×C11)⋊(C3×D159)
unambiguous semidirect product(C2×C53)⋊(C3×D33)

Splittings

Fitting, socleC2×C32×C11×C53 ⋊ C2
derivedC3×C11×C53 ⋊ C22×C3
HallC32×C11×C53 ⋊ C22
HallC11×C53 ⋊ C2×C3×D3
HallC32×C53 ⋊ C2×D11
HallC32×C11 ⋊ C2×D53
SylowC53 ⋊ C2×C3×D33
SylowC11 ⋊ C2×C3×D159
SylowC32 ⋊ C2×D583

Subgroups

subgroupG/H
center, hypercenterC2×C3D1749
commutator, cosocle, hypocenterC3×C11×C53C22×C3
FrattiniC1G
Fitting, socleC2×C32×C11×C53C2
LCSG ▷ C3×C11×C53
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6996

Conjugacy classes & character table

5256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20988, 84);