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C2×C13⋊C3×D205 #44544390

order31980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊C3×D205
unambiguous semidirect product(C2×C5)⋊(C13⋊C3×D41)
unambiguous semidirect product(C2×C41)⋊(D5×C13⋊C3)
unambiguous semidirect product(C2×C13×D205)⋊C3

Splittings

Fitting, socleC2×C5×C13×C41 ⋊ C2×C3
derived, HallC5×C13×C41 ⋊ C22×C3
HallC2×C13×D205 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C22
HallC13⋊C3×C41 ⋊ C2×D5
HallC13×C41 ⋊ C2×C3×D5
HallC5×C41 ⋊ C22×C13⋊C3
HallC5×C13⋊C3 ⋊ C2×D41
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×C3×D205
SylowC5 ⋊ C2×C13⋊C3×D41

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×D205
commutator, cosocle, hypocenterC5×C13×C41C22×C3
FrattiniC1G
Fitting, socleC2×C5×C13×C41C2×C3
LCSG ▷ C5×C13×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5330

Conjugacy classes & character table

1456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 118);