Finite Group Databasebeta

← Prev (#36339708) Next (#36339710) →

C11⋊(C25⋊(D13⋊C3)) #36339709

order21450
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(C25⋊(D13⋊C3))
unambiguous semidirect productC25⋊(C11⋊(D13⋊C3))
unambiguous semidirect product(C13⋊C3)⋊D275
unambiguous semidirect productD3575⋊C3

Splittings

Fitting, derived, HallC11×C13×C25 ⋊ C2×C3
HallC11×C25×C13⋊C3 ⋊ C2
HallD3575 ⋊ C3
HallC25×C13⋊C3 ⋊ D11
HallC11×C13⋊C3 ⋊ D25
HallC13×C25 ⋊ C3×D11
HallC11×C25 ⋊ D13⋊C3
HallC11×C13 ⋊ C3×D25
HallC13⋊C3 ⋊ D275
SylowC25 ⋊ C11⋊(D13⋊C3)
SylowC13 ⋊ C3×D275
SylowC11 ⋊ C25⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C13×C25C2×C3
FrattiniC5C5⋊(C11⋊(D13⋊C3))
socleC5×C11×C13C3×D5
LCSG ▷ C11×C13×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 3575

A minimal faithful permutation representation — 2 generators on 49 points:

(2,6,7,3,4,8)(5,12,11,9,10,13)(15,16)(17,18)(19,20)(21,22)(23,24)(26,28)(27,31)(29,34)(30,37)(32,40)(33,39)(35,36)(38,44)(41,45)(42,46)(43,48)(47,49);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,17,19,21,23,24,22,20,18,16)(25,39,49,42,28,31,45,43,34,37,40,38,36,35,44,32,30,29,48,41,27,26,46,47,33)

Polycyclic presentation:

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

Conjugacy classes & character table

967 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 33);