Finite Group Databasebeta

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C2×C3×C13×D41⋊C5 #44544377

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C13×D41⋊C5
unambiguous semidirect productD41⋊(C2×C3×C5×C13)
unambiguous semidirect product(C2×D41)⋊(C3×C5×C13)
unambiguous semidirect product(C41⋊C5)⋊(C22×C3×C13)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C3×C13)
unambiguous semidirect product(C2×C3×D41)⋊(C5×C13)
unambiguous semidirect product(C2×C3×C13×D41)⋊C5

Splittings

Fitting, socleC2×C3×C13×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C3×C5×C13
HallC3×C13×C41⋊C5 ⋊ C22
HallC2×C3×C13×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C22×C3
HallC2×C13×D41 ⋊ C3×C5
HallC3×C13×C41 ⋊ C22×C5
HallC3×C41⋊C5 ⋊ C22×C13
HallC13×C41 ⋊ C22×C3×C5
HallC2×C3×D41 ⋊ C5×C13
HallC41⋊C5 ⋊ C22×C3×C13
HallC2×D41 ⋊ C3×C5×C13
HallC3×C41 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D41⋊C5
commutator, cosocle, hypocenterC41C22×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C13×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3198

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 105);