Finite Group Databasebeta

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D13×D15×C43 #46776573

order33540
automorphism?
homologyAbelianization (H1) = C22×C43 · Schur multiplier (H2) = C2

Aliases

direct productD13×D15×C43
unambiguous semidirect product(C3×D13)⋊(D5×C43)
unambiguous semidirect product(C5×D13)⋊(D3×C43)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C22
derived, HallC3×C5×C13 ⋊ C22×C43
HallC5×C13×C43 ⋊ C2×D3
HallC3×C13×C43 ⋊ C2×D5
HallC3×C5×C43 ⋊ C2×D13
HallC13×C43 ⋊ C2×D15
HallC5×C43 ⋊ D3×D13
HallC3×C43 ⋊ D5×D13
HallC5×C13 ⋊ C2×D3×C43
HallC3×C13 ⋊ C2×D5×C43
HallC3×C5 ⋊ C2×D13×C43
SylowC13 ⋊ C2×D15×C43
SylowC5 ⋊ D3×D13×C43
SylowC3 ⋊ D5×D13×C43

Subgroups

subgroupG/H
center, hypercenterC43D13×D15
commutator, cosocle, hypocenterC3×C5×C13C22×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C43

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

3096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 193);