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C5×D13⋊C3×D41 #44544347

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D13⋊C3×D41
unambiguous semidirect productD13⋊(C3×C5×D41)
unambiguous semidirect product(C5×D13×D41)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C22×C3
derived, HallC13×C41 ⋊ C22×C3×C5
HallC5×D13×D41 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C22
HallD13×D41 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C22×C5
HallC5×C41 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C2×D41
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ C2×C5×D13⋊C3
HallC13⋊C3 ⋊ C2×C5×D41
SylowC13 ⋊ C2×C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC5D13⋊C3×D41
commutator, cosocle, hypocenterC13×C41C22×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C41C22×C3
LCSG ▷ C13×C41
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 75);