Finite Group Databasebeta

← Prev (#44539540) Next (#44539542) →

C5⋊((D211⋊C3)⋊C5) #44539541

order31650
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊((D211⋊C3)⋊C5)
unambiguous semidirect product((C211⋊C3)⋊C5)⋊D5
unambiguous semidirect product(C5⋊(D211⋊C3))⋊C5
unambiguous semidirect product(C5⋊(D211⋊C5))⋊C3

Splittings

Fitting, socle, derivedC5×C211 ⋊ C2×C3×C5
HallC5×(C211⋊C3)⋊C5 ⋊ C2
HallC5⋊(D211⋊C5) ⋊ C3
HallC5×C211⋊C5 ⋊ C2×C3
HallC211⋊C3 ⋊ C5×D5
SylowC211 ⋊ C3×C5×D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C211C2×C3×C5
LCSG ▷ C5×C211
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1055

Polycyclic presentation:

2,3,5^2,211|d^a=d^4,e^a=e^210,e^b=e^14,e^c=e^188

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31650, 21);