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(C5⋊(D43⋊C3))⋊D13 #46776504

order33540
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊(D43⋊C3))⋊D13
unambiguous semidirect product((C43⋊C3)⋊D13)⋊D5

Splittings

Fitting, socle, derived, HallC5×C13×C43 ⋊ C22×C3
HallD65⋊D43 ⋊ C3
HallC5×C13×C43⋊C3 ⋊ C22
HallC13×C43⋊C3 ⋊ C2×D5
HallC5×C43⋊C3 ⋊ C2×D13
HallC13×C43 ⋊ C2×C3×D5
HallC5×C43 ⋊ C2×C3×D13
HallC43⋊C3 ⋊ D5×D13
HallC5×C13 ⋊ C2×D43⋊C3
SylowC43 ⋊ C3×D5×D13
SylowC13 ⋊ D5×D43⋊C3
SylowC5 ⋊ D13×D43⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C43C22×C3
LCSG ▷ C5×C13×C43
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2795

Polycyclic presentation:

2^2,3,5,13,43|e^a=e^12,f^a=f^42,d^b=d^4,e^b=e^12,f^c=f^36

Conjugacy classes & character table

334 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 124);