Finite Group Databasebeta

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C5×C22⋊#13131976 #46776596

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

Aliases

direct productC5×C22⋊#13131976
unambiguous semidirect productC22⋊(C5×#13131976)
unambiguous semidirect product(C22×C5)⋊#13131976

Splittings

Fitting, socle, HallC22×C5×C13×C43 ⋊ C3
derived, HallC22×C13×C43 ⋊ C3×C5
HallC5×C13×C43 ⋊ A4
HallC22×C5×C43 ⋊ C13⋊C3
HallC13×C43 ⋊ C5×A4
HallC22×C5×C13 ⋊ C43⋊C3
HallC5×C43 ⋊ C22⋊(C13⋊C3)
HallC22×C43 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C22⋊(C43⋊C3)
HallC22×C13 ⋊ C5×C43⋊C3
SylowC43 ⋊ C5×C22⋊(C13⋊C3)
HallC22×C5 ⋊ #13131976
SylowC13 ⋊ C5×C22⋊(C43⋊C3)
SylowC22 ⋊ C5×#13131976

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#13131976
commutator, cosocle, hypocenterC22×C13×C43C3×C5
FrattiniC1G
Fitting, socleC22×C5×C13×C43C3
LCSG ▷ C22×C13×C43
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

3740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 216);