Finite Group Databasebeta

← Prev (#26044590) Next (#26044592) →

C3⋊(C3⋊(D131⋊C5)) #26044591

order11790
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(D131⋊C5))
unambiguous semidirect product(C131⋊C5)⋊(C3⋊D3)
unambiguous semidirect product(C3⋊D393)⋊C5

Splittings

Fitting, socle, derived, HallC32×C131 ⋊ C2×C5
HallC32×C131⋊C5 ⋊ C2
HallC3⋊D393 ⋊ C5
HallC131⋊C5 ⋊ C3⋊D3
SylowC131 ⋊ C5×C3⋊D3
SylowC32 ⋊ D131⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C131C2×C5
LCSG ▷ C32×C131
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,5,3^2,131|c^a=c^2,d^a=d^2,e^a=e^130,e^b=e^58

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊(D131⋊C5), C3⋊D3×D131⋊C5, C2×C3⋊(C3⋊(D131⋊C5))
maximal normal subgroup ofD3×C3⋊(D131⋊C5), C3⋊D3×D131⋊C5, C2×C3⋊(C3⋊(D131⋊C5))
maximal quotient ofC3⋊(C3⋊(Dic131⋊C5)), C2×C3⋊(C3⋊(D131⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11790, 17);