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C5×C13×C22⋊(C43⋊C3) #46776594

order33540
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C13×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C5×C13×C43⋊C3)
unambiguous semidirect product(C22×C5)⋊(C13×C43⋊C3)
unambiguous semidirect productC43⋊(C5×A4×C13)
unambiguous semidirect product(C5×C43)⋊(A4×C13)

Splittings

Fitting, socle, HallC22×C5×C13×C43 ⋊ C3
derived, HallC22×C43 ⋊ C3×C5×C13
HallC5×C13×C43 ⋊ A4
HallC22×C13×C43 ⋊ C3×C5
HallC22×C5×C43 ⋊ C3×C13
HallC13×C43 ⋊ C5×A4
HallC22×C5×C13 ⋊ C43⋊C3
HallC5×C43 ⋊ A4×C13
HallC22×C13 ⋊ C5×C43⋊C3
SylowC43 ⋊ C5×A4×C13
HallC22×C5 ⋊ C13×C43⋊C3
SylowC22 ⋊ C5×C13×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C13C22⋊(C43⋊C3)
commutator, cosocle, hypocenterC22×C43C3×C5×C13
FrattiniC1G
Fitting, socleC22×C5×C13×C43C3
LCSG ▷ C22×C43
UCSC1 ◁ C5×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 214);