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C3×D13×D41⋊C5 #44544326

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

Aliases

direct productC3×D13×D41⋊C5
unambiguous semidirect productD41⋊(C3×C5×D13)
unambiguous semidirect product(C3×D13×D41)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C22×C5
derived, HallC13×C41 ⋊ C22×C3×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallC3×D13×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C22×C3
HallD13×D41 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ C2×D13
HallC41⋊C5 ⋊ C2×C3×D13
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C2×C3×C5×D13
HallC3×C13 ⋊ C2×D41⋊C5
SylowC13 ⋊ C2×C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D13×D41⋊C5
commutator, cosocle, hypocenterC13×C41C22×C3×C5
FrattiniC1G
Fitting, socleC3×C13×C41C22×C5
LCSG ▷ C13×C41
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 54);