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C2×D39×C41⋊C5 #44544383

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

Aliases

direct productC2×D39×C41⋊C5
unambiguous semidirect product(C2×C3)⋊(D13×C41⋊C5)
unambiguous semidirect product(C2×C13)⋊(D3×C41⋊C5)
unambiguous semidirect product(C2×C41×D39)⋊C5

Splittings

Fitting, socleC2×C3×C13×C41 ⋊ C2×C5
derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallC2×C41×D39 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C2×C5×D39
HallC3×C13 ⋊ C22×C41⋊C5
SylowC13 ⋊ C2×D3×C41⋊C5
SylowC3 ⋊ C2×D13×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D39×C41⋊C5
commutator, cosocle, hypocenterC3×C13×C41C22×C5
FrattiniC1G
Fitting, socleC2×C3×C13×C41C2×C5
LCSG ▷ C3×C13×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3198

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 111);