Finite Group Databasebeta

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C3⋊(C3⋊#16811774) #44501835

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

Aliases

unambiguous semidirect productC3⋊(C3⋊#16811774)

Splittings

Fitting, socle, derived, HallC32×C11×C31 ⋊ C2×C5
HallC32×#13133724 ⋊ C2
HallC11×C3⋊D93 ⋊ C5
Hall#13133724 ⋊ C3⋊D3
HallC3⋊D93 ⋊ C11⋊C5
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ C2×C11⋊C5
HallC32×C11 ⋊ D31⋊C5
SylowC31 ⋊ C3⋊D3×C11⋊C5
SylowC11 ⋊ C3⋊(C3⋊(D31⋊C5))
SylowC32 ⋊ #16811774

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,f^a=f^30,e^b=e^4,f^b=f^2

Conjugacy classes & character table

339 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 202);