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C5×C31×C22⋊(C13⋊C3) #37563992

order24180
automorphism?
homologyAbelianization (H1) = C3×C5×C31 · Schur multiplier (H2) = C2

Aliases

direct productC5×C31×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C5×C31×C13⋊C3)
unambiguous semidirect productC13⋊(C5×A4×C31)
unambiguous semidirect product(C22×C5)⋊(C31×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(A4×C31)

Splittings

Fitting, socle, HallC22×C5×C13×C31 ⋊ C3
derived, HallC22×C13 ⋊ C3×C5×C31
HallC5×C13×C31 ⋊ A4
HallC22×C13×C31 ⋊ C3×C5
HallC22×C5×C31 ⋊ C13⋊C3
HallC13×C31 ⋊ C5×A4
HallC22×C5×C13 ⋊ C3×C31
HallC22×C31 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ A4×C31
HallC22×C5 ⋊ C31×C13⋊C3
SylowC13 ⋊ C5×A4×C31
SylowC22 ⋊ C5×C31×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C31C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C5×C31
FrattiniC1G
Fitting, socleC22×C5×C13×C31C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C31

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

3100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 291);