Finite Group Databasebeta

← Prev (#36339791) Next (#36339793) →

C3⋊(C5⋊D715) #36339792

order21450
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC3⋊(C5⋊D715)
unambiguous semidirect productC5⋊D2145
unambiguous semidirect productC11⋊(C3⋊(C5⋊D65))
unambiguous semidirect productC13⋊(C3⋊(C5⋊D55))

Splittings

Fitting, socle, derived, HallC3×C52×C11×C13 ⋊ C2
HallC52×C11×C13 ⋊ D3
HallC3×C52×C13 ⋊ D11
HallC3×C52×C11 ⋊ D13
HallC3×C11×C13 ⋊ C5⋊D5
HallC52×C13 ⋊ D33
HallC52×C11 ⋊ D39
HallC11×C13 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ D143
HallC3×C13 ⋊ C5⋊D55
HallC3×C11 ⋊ C5⋊D65
SylowC52 ⋊ D429
SylowC13 ⋊ C3⋊(C5⋊D55)
SylowC11 ⋊ C3⋊(C5⋊D65)
SylowC3 ⋊ C5⋊D715

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C11×C13C2
LCSG ▷ C3×C52×C11×C13
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Polycyclic presentation:

2,3,5^2,11,13|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^12

Conjugacy classes & character table

5364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 116);