Finite Group Databasebeta

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C13⋊C3×#4223⋊C5 #44544316

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×#4223⋊C5
unambiguous semidirect product#4223⋊(C5×C13⋊C3)
unambiguous semidirect product(C13⋊C3×#4223)⋊C5
unambiguous semidirect product(C13×#4223⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C3×C4×C5
HallC13×#4223⋊C5 ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C4
HallC13⋊C3×#4223 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC13×#4223 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC41⋊C5 ⋊ C4×C13⋊C3
Hall#4223 ⋊ C5×C13⋊C3
SylowC41 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×#4223⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C41C3×C4×C5
prime radicalC13⋊C3×D41⋊C5C2
cosocleC13×D41C2×C3×C5
LCSG ▷ C13×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 44);