Finite Group Databasebeta

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C11×C5⋊(D31⋊C9) #44501709

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

Aliases

direct productC11×C5⋊(D31⋊C9)
unambiguous semidirect productC5⋊(C11×D31⋊C9)
unambiguous semidirect product(C31⋊C9)⋊(D5×C11)
unambiguous semidirect productD155⋊(C9×C11)
unambiguous semidirect product(C11×D155)⋊C9

Splittings

derived, HallC5×C31 ⋊ C2×C9×C11
HallC5×C11×C31⋊C9 ⋊ C2
HallC11×D155 ⋊ C9
HallC11×C31⋊C9 ⋊ D5
HallC5×C11×C31 ⋊ C2×C9
HallC5×C31⋊C9 ⋊ C2×C11
HallC11×C31 ⋊ C9×D5
HallD155 ⋊ C9×C11
HallC31⋊C9 ⋊ D5×C11
HallC5×C11 ⋊ D31⋊C9
SylowC31 ⋊ C9×D5×C11
SylowC5 ⋊ C11×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C2×C9×C11
FrattiniC3C11×C5⋊(D31⋊C3)
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×C11×D155C3
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

1221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 76);