Finite Group Databasebeta

← Prev (#44544461) Next (#44544463) →

D41×D195 #44544462

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

Aliases

direct productD41×D195
unambiguous semidirect product(C3×D41)⋊D65
unambiguous semidirect product(C5×D41)⋊D39
unambiguous semidirect product(C13×D41)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C13×C41 ⋊ C22
HallC5×C13×C41 ⋊ C2×D3
HallC3×C13×C41 ⋊ C2×D5
HallC3×C5×C41 ⋊ C2×D13
HallC13×C41 ⋊ C2×D15
HallC5×C41 ⋊ C2×D39
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×D65
HallC5×C13 ⋊ D3×D41
SylowC41 ⋊ C2×D195
HallC3×C13 ⋊ D5×D41
HallC3×C5 ⋊ D13×D41
SylowC13 ⋊ D15×D41
SylowC5 ⋊ D39×D41
SylowC3 ⋊ D41×D65

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C41C22
LCSG ▷ C3×C5×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 190);