Finite Group Databasebeta

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C5×D3×D13×C41 #44544435

order31980
automorphism?
homologyAbelianization (H1) = C22×C5×C41 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D13×C41
unambiguous semidirect product(D3×C13)⋊(C2×C5×C41)
unambiguous semidirect product(C3×D13)⋊(C2×C5×C41)
unambiguous semidirect productD39⋊(C2×C5×C41)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C22
derived, HallC3×C13 ⋊ C22×C5×C41
HallC5×C13×C41 ⋊ C2×D3
HallC3×C13×C41 ⋊ C22×C5
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC3×C5×C13 ⋊ C22×C41
HallC3×C41 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D3×C41
HallC3×C5 ⋊ C2×D13×C41
SylowC13 ⋊ C2×C5×D3×C41
SylowC3 ⋊ C2×C5×D13×C41

Subgroups

subgroupG/H
center, hypercenterC5×C41D3×D13
commutator, cosocle, hypocenterC3×C13C22×C5×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C22
LCSG ▷ C3×C13
UCSC1 ◁ C5×C41

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 163);