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C3×D41×D65 #44544422

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

Aliases

direct productC3×D41×D65
unambiguous semidirect product(C5×D41)⋊(C3×D13)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C22
derived, HallC5×C13×C41 ⋊ C22×C3
HallC3×C13×C41 ⋊ C2×D5
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×C3×D5
HallC5×C41 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×D65
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ C2×C3×D65
HallC3×C13 ⋊ D5×D41
HallC3×C5 ⋊ D13×D41
SylowC13 ⋊ C3×D5×D41
SylowC5 ⋊ C3×D13×D41

Subgroups

subgroupG/H
center, hypercenterC3D41×D65
commutator, cosocle, hypocenterC5×C13×C41C22×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C41C22
LCSG ▷ C5×C13×C41
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 150);