Finite Group Databasebeta

← Prev (#37563804) Next (#37563806) →

D39×D31⋊C5 #37563805

order24180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD39×D31⋊C5
unambiguous semidirect productD31⋊(C5×D39)
unambiguous semidirect product(C3×D31⋊C5)⋊D13
unambiguous semidirect product(C13×D31⋊C5)⋊D3
unambiguous semidirect product(D31×D39)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C31 ⋊ C22×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C22
HallD31×D39 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D13
HallC13×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ C2×D39
HallC3×C31 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D39
SylowC13 ⋊ D3×D31⋊C5
SylowC3 ⋊ D13×D31⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C31C22×C5
LCSG ▷ C3×C13×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 104);