Finite Group Databasebeta

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D5×C13×D129 #46776578

order33540
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productD5×C13×D129
unambiguous semidirect product(C3×D5)⋊(C13×D43)
unambiguous semidirect product(D5×C43)⋊(D3×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C22
derived, HallC3×C5×C43 ⋊ C22×C13
HallC5×C13×C43 ⋊ C2×D3
HallC3×C13×C43 ⋊ C2×D5
HallC13×C43 ⋊ D3×D5
HallC5×C43 ⋊ C2×D3×C13
HallC3×C5×C13 ⋊ C2×D43
HallC3×C43 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×D129
SylowC43 ⋊ D3×D5×C13
HallC3×C13 ⋊ D5×D43
HallC3×C5 ⋊ C2×C13×D43
SylowC5 ⋊ C2×C13×D129
SylowC3 ⋊ D5×C13×D43

Subgroups

subgroupG/H
center, hypercenterC13D5×D129
commutator, cosocle, hypocenterC3×C5×C43C22×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C43C22
LCSG ▷ C3×C5×C43
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

3432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 198);