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C5×D13×D43⋊C3 #46776441

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D13×D43⋊C3
unambiguous semidirect productD43⋊(C3×C5×D13)
unambiguous semidirect product(C13×D43⋊C3)⋊(C2×C5)
unambiguous semidirect product(D13×C43⋊C3)⋊(C2×C5)
unambiguous semidirect product((C43⋊C3)⋊D13)⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C13×C43 ⋊ C22×C3
derived, HallC13×C43 ⋊ C22×C3×C5
HallC5×D13×D43 ⋊ C3
HallC5×C13×C43⋊C3 ⋊ C22
HallD13×D43 ⋊ C3×C5
HallC13×C43⋊C3 ⋊ C22×C5
HallC5×C43⋊C3 ⋊ C2×D13
HallC5×C43 ⋊ C2×C3×D13
HallC43⋊C3 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D43⋊C3
SylowC43 ⋊ C2×C3×C5×D13
SylowC13 ⋊ C2×C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D13×D43⋊C3
commutator, cosocle, hypocenterC13×C43C22×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C43C22×C3
LCSG ▷ C13×C43
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2795

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 61);