Finite Group Databasebeta

← Prev (#44539311) Next (#44539313) →

D5×C17×D31⋊C3 #44539312

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productD5×C17×D31⋊C3
unambiguous semidirect productD31⋊(C3×D5×C17)
unambiguous semidirect product(D5×D31)⋊(C3×C17)
unambiguous semidirect product(C5×D31⋊C3)⋊(C2×C17)
unambiguous semidirect product(D5×C31⋊C3)⋊(C2×C17)
unambiguous semidirect product(C5⋊(D31⋊C3))⋊(C2×C17)
unambiguous semidirect product(D5×C17×D31)⋊C3

Splittings

Fitting, socle, HallC5×C17×C31 ⋊ C22×C3
derived, HallC5×C31 ⋊ C22×C3×C17
HallD5×C17×D31 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C22
HallC17×C31⋊C3 ⋊ C2×D5
HallD5×D31 ⋊ C3×C17
HallC17×C31 ⋊ C2×C3×D5
HallC5×C31⋊C3 ⋊ C22×C17
HallC31⋊C3 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×D5×C17
SylowC5 ⋊ C2×C17×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D5×D31⋊C3
commutator, cosocle, hypocenterC5×C31C22×C3×C17
FrattiniC1G
Fitting, socleC5×C17×C31C22×C3
LCSG ▷ C5×C31
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2635

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 69);