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C22⋊(C13⋊C3)×C41⋊C5 #44544340

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

Aliases

direct productC22⋊(C13⋊C3)×C41⋊C5
unambiguous semidirect productC22⋊(C13⋊C3×C41⋊C5)
unambiguous semidirect productC13⋊(A4×C41⋊C5)
unambiguous semidirect productC41⋊(C5×C22⋊(C13⋊C3))
unambiguous semidirect product(C22×C41⋊C5)⋊(C13⋊C3)
unambiguous semidirect product(C13×C41⋊C5)⋊A4
unambiguous semidirect product(C41×C22⋊(C13⋊C3))⋊C5

Splittings

Fitting, socle, derived, HallC22×C13×C41 ⋊ C3×C5
HallC22×C13×C41⋊C5 ⋊ C3
HallC41×C22⋊(C13⋊C3) ⋊ C5
HallC13×C41⋊C5 ⋊ A4
HallC22×C41⋊C5 ⋊ C13⋊C3
HallC13×C41 ⋊ C5×A4
HallC22×C41 ⋊ C5×C13⋊C3
HallC22×C13 ⋊ C3×C41⋊C5
SylowC41 ⋊ C5×C22⋊(C13⋊C3)
SylowC13 ⋊ A4×C41⋊C5
SylowC22 ⋊ C13⋊C3×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C13×C41C3×C5
LCSG ▷ C22×C13×C41
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 68);