Finite Group Databasebeta

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C2×C5×C43×D13⋊C3 #46776507

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C43 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C43×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C5×C43)
unambiguous semidirect product(C13⋊C3)⋊(C22×C5×C43)
unambiguous semidirect product(C2×D13)⋊(C3×C5×C43)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C5×C43)
unambiguous semidirect product(C2×C5×D13)⋊(C3×C43)

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C5×C43
HallC2×C5×D13×C43 ⋊ C3
HallC5×C13⋊C3×C43 ⋊ C22
HallC5×C13×C43 ⋊ C22×C3
HallC2×D13×C43 ⋊ C3×C5
HallC13⋊C3×C43 ⋊ C22×C5
HallC13×C43 ⋊ C22×C3×C5
HallC2×C5×D13 ⋊ C3×C43
HallC5×C13⋊C3 ⋊ C22×C43
HallC5×C13 ⋊ C22×C3×C43
HallC2×D13 ⋊ C3×C5×C43
HallC13⋊C3 ⋊ C22×C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C5×C43D13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C5×C43
FrattiniC1G
Fitting, socleC2×C5×C13×C43C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C43

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 127);