Finite Group Databasebeta

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C3⋊(C5⋊(C11⋊(D31⋊C3))) #44501858

order30690
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C5⋊(C11⋊(D31⋊C3)))
unambiguous semidirect productC5⋊(C3⋊(C11⋊(D31⋊C3)))
unambiguous semidirect productC11⋊(C3⋊(C5⋊(D31⋊C3)))
unambiguous semidirect product(C31⋊C3)⋊D165
unambiguous semidirect productD5115⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C31 ⋊ C2×C3
HallC3×C5×C11×C31⋊C3 ⋊ C2
HallC3×C11×C31⋊C3 ⋊ D5
HallC5×C11×C31 ⋊ C3×D3
HallC3×C5×C31⋊C3 ⋊ D11
HallC11×C31 ⋊ C3×D15
HallC3×C31⋊C3 ⋊ D55
HallC5×C31 ⋊ C3×D33
HallC5×C11 ⋊ C3⋊(D31⋊C3)
SylowC31 ⋊ C3×D165
SylowC11 ⋊ C3⋊(C5⋊(D31⋊C3))
SylowC5 ⋊ C3⋊(C11⋊(D31⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C31C2×C3
LCSG ▷ C3×C5×C11×C31
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5115

Polycyclic presentation:

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

Conjugacy classes & character table

1077 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 225);