Finite Group Databasebeta

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C5⋊(C11⋊(D31⋊C9)) #44501711

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

Aliases

unambiguous semidirect productC5⋊(C11⋊(D31⋊C9))
unambiguous semidirect productC11⋊(C5⋊(D31⋊C9))
unambiguous semidirect product(C31⋊C9)⋊D55
unambiguous semidirect productD1705⋊C9

Splittings

derived, HallC5×C11×C31 ⋊ C2×C9
HallC5×C11×C31⋊C9 ⋊ C2
HallD1705 ⋊ C9
HallC11×C31⋊C9 ⋊ D5
HallC5×C31⋊C9 ⋊ D11
HallC11×C31 ⋊ C9×D5
HallC31⋊C9 ⋊ D55
HallC5×C31 ⋊ C9×D11
HallC5×C11 ⋊ D31⋊C9
SylowC31 ⋊ C9×D55
SylowC11 ⋊ C5⋊(D31⋊C9)
SylowC5 ⋊ C11⋊(D31⋊C9)

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C5⋊(C11⋊(D31⋊C3))
commutator, hypocenterC5×C11×C31C2×C9
Fitting, socle, cosocleC3×C5×C11×C31C2×C3
prime radicalC3×D1705C3
LCSG ▷ C5×C11×C31
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Polycyclic presentation:

2,3,5,11,31,3|b^3=f,c^a=c^4,d^a=d^10,e^a=e^30,e^b=e^25

Conjugacy classes & character table

1086 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 78);