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C3⋊(((C31⋊C3)⋊C5)⋊D11) #44501771

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(((C31⋊C3)⋊C5)⋊D11)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊D33
unambiguous semidirect product(C3⋊(ΓL(1,𝔽32)⋊D11))⋊C3

Splittings

Fitting, socle, derivedC3×C11×C31 ⋊ C2×C3×C5
HallC3×C11×(C31⋊C3)⋊C5 ⋊ C2
HallC3⋊(C11⋊(D31⋊C3)) ⋊ C5
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×(C31⋊C3)⋊C5 ⋊ D11
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C5×D11
HallΓL(1,𝔽32) ⋊ C3×D33
SylowC31 ⋊ C3×C5×D33
SylowC11 ⋊ C3⋊AGL(1,𝔽31)

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Polycyclic presentation:

2,3,5,3,11,31|d^a=d^2,e^a=e^10,f^a=f^30,f^b=f^5,f^c=f^16

Conjugacy classes & character table

303 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 138);