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C3⋊(#16811772⋊C3) #44501764

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

Aliases

unambiguous semidirect productC3⋊(#16811772⋊C3)
unambiguous semidirect product(C3⋊#16811772)⋊C3

Splittings

Fitting, socle, derivedC3×C11×C31 ⋊ C2×C3×C5
HallC3×#13133723⋊C3 ⋊ C2
HallC11×C3⋊(D31⋊C3) ⋊ C5
HallC3×C11×C31⋊C3 ⋊ C2×C5
Hall#13133723 ⋊ C3×D3
HallC3⋊(D31⋊C3) ⋊ C11⋊C5
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C2×C11⋊C5
SylowC31 ⋊ C3×D3×C11⋊C5
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,f^a=f^30,f^b=f^5,e^c=e^4,f^c=f^8

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 131);