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C5×C43×C22⋊(C13⋊C3) #46776595

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

Aliases

direct productC5×C43×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C5×C13⋊C3×C43)
unambiguous semidirect productC13⋊(C5×A4×C43)
unambiguous semidirect product(C22×C5)⋊(C13⋊C3×C43)
unambiguous semidirect product(C5×C13)⋊(A4×C43)

Splittings

Fitting, socle, HallC22×C5×C13×C43 ⋊ C3
derived, HallC22×C13 ⋊ C3×C5×C43
HallC5×C13×C43 ⋊ A4
HallC22×C13×C43 ⋊ C3×C5
HallC22×C5×C43 ⋊ C13⋊C3
HallC13×C43 ⋊ C5×A4
HallC22×C5×C13 ⋊ C3×C43
HallC22×C43 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ A4×C43
HallC22×C5 ⋊ C13⋊C3×C43
SylowC13 ⋊ C5×A4×C43
SylowC22 ⋊ C5×C13⋊C3×C43

Subgroups

subgroupG/H
center, hypercenterC5×C43C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C5×C43
FrattiniC1G
Fitting, socleC22×C5×C13×C43C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C43

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

4300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 215);