Finite Group Databasebeta

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C2×C13⋊C3×D209 #45656769

order32604
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊C3×D209
unambiguous semidirect product(C2×C11)⋊(D19×C13⋊C3)

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2×C3
derived, HallC11×C13×C19 ⋊ C22×C3
HallC2×C13×D209 ⋊ C3
HallC11×C19×C13⋊C3 ⋊ C22
HallC19×C13⋊C3 ⋊ C2×D11
HallC11×C13⋊C3 ⋊ C2×D19
HallC13×C19 ⋊ C2×C3×D11
HallC11×C19 ⋊ C22×C13⋊C3
HallC11×C13 ⋊ C2×C3×D19
SylowC19 ⋊ C2×D11×C13⋊C3
SylowC13 ⋊ C2×C3×D209
SylowC11 ⋊ C2×D19×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×D209
commutator, cosocle, hypocenterC11×C13×C19C22×C3
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2×C3
LCSG ▷ C11×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5434

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 119);