Finite Group Databasebeta

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C3⋊(C3⋊#16811780) #44501829

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

Aliases

unambiguous semidirect productC3⋊(C3⋊#16811780)

Splittings

Fitting, socle, derived, HallC32×C11×C31 ⋊ C2×C5
HallC32×#13133724 ⋊ C2
HallC31×C3⋊D33 ⋊ C5
Hall#13133724 ⋊ C3⋊D3
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ AGL(1,𝔽11)
HallC3⋊D33 ⋊ ΓL(1,𝔽32)
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3⋊(C3⋊AGL(1,𝔽11))
SylowC11 ⋊ C3⋊D3×ΓL(1,𝔽32)
SylowC32 ⋊ #16811780

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C31C2×C5
LCSG ▷ C32×C11×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Polycyclic presentation:

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

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 196);