Finite Group Databasebeta

← Prev (#44501707) Next (#44501709) →

D5×C11×C31⋊C9 #44501708

order30690
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×C31⋊C9
unambiguous semidirect productC5⋊(C2×C11×C31⋊C9)
unambiguous semidirect product(D5×C31)⋊(C9×C11)
unambiguous semidirect product(D5×C11×C31)⋊C9

Splittings

derived, HallC5×C31 ⋊ C2×C9×C11
HallC5×C11×C31⋊C9 ⋊ C2
HallD5×C11×C31 ⋊ C9
HallC5×C11×C31 ⋊ C2×C9
HallC5×C31⋊C9 ⋊ C2×C11
HallC11×C31 ⋊ C9×D5
HallD5×C31 ⋊ C9×C11
HallC5×C11 ⋊ C2×C31⋊C9
SylowC31 ⋊ C9×D5×C11
SylowC5 ⋊ C2×C11×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×C31⋊C3
commutator, hypocenterC5×C31C2×C9×C11
FrattiniC3D5×C11×C31⋊C3
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×D5×C11×C31C3
cosocleC3×C5×C31C2×C3×C11
LCSG ▷ C5×C31
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 75);