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A4×C13×C41⋊C5 #44544339

order31980
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productA4×C13×C41⋊C5
unambiguous semidirect productC22⋊(C3×C13×C41⋊C5)
unambiguous semidirect productC41⋊(C5×A4×C13)
unambiguous semidirect product(A4×C41)⋊(C5×C13)
unambiguous semidirect product(C22×C41⋊C5)⋊(C3×C13)
unambiguous semidirect product(A4×C13×C41)⋊C5

Splittings

Fitting, socle, HallC22×C13×C41 ⋊ C3×C5
derived, HallC22×C41 ⋊ C3×C5×C13
HallC22×C13×C41⋊C5 ⋊ C3
HallA4×C13×C41 ⋊ C5
HallC22×C41⋊C5 ⋊ C3×C13
HallC13×C41 ⋊ C5×A4
HallA4×C41 ⋊ C5×C13
HallC22×C13 ⋊ C3×C41⋊C5
SylowC41 ⋊ C5×A4×C13
SylowC22 ⋊ C3×C13×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC13A4×C41⋊C5
commutator, cosocle, hypocenterC22×C41C3×C5×C13
FrattiniC1G
Fitting, socleC22×C13×C41C3×C5
LCSG ▷ C22×C41
UCSC1 ◁ C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 67);