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Dic13⋊C3×C41⋊C5 #44544307

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

Aliases

direct productDic13⋊C3×C41⋊C5
unambiguous semidirect productDic13⋊(C3×C41⋊C5)
unambiguous semidirect product(C41×Dic13⋊C3)⋊C5
unambiguous semidirect product(Dic13×C41⋊C5)⋊C3

Splittings

derived, HallC13×C41 ⋊ C3×C4×C5
HallDic13×C41⋊C5 ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C4
HallC41×Dic13⋊C3 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC41×Dic13 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallDic13 ⋊ C3×C41⋊C5
SylowC41 ⋊ C5×Dic13⋊C3
HallC13⋊C3 ⋊ C4×C41⋊C5
SylowC13 ⋊ C3×C4×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D13⋊C3×C41⋊C5
commutator, hypocenterC13×C41C3×C4×C5
Fitting, socle, cosocleC2×C13×C41C2×C3×C5
prime radicalC2×C13⋊C3×C41⋊C5C2
LCSG ▷ C13×C41
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 35);