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C13×C3⋊(Dic41⋊C5) #44544296

order31980
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(Dic41⋊C5)
unambiguous semidirect productC3⋊(C13×Dic41⋊C5)
unambiguous semidirect productDic123⋊(C5×C13)
unambiguous semidirect product(C13×Dic123)⋊C5

Splittings

derived, HallC3×C41 ⋊ C4×C5×C13
HallC3×C13×C41⋊C5 ⋊ C4
HallC13×Dic123 ⋊ C5
HallC13×C41⋊C5 ⋊ Dic3
HallC3×C13×C41 ⋊ C4×C5
HallC3×C41⋊C5 ⋊ C4×C13
HallC13×C41 ⋊ C5×Dic3
HallDic123 ⋊ C5×C13
HallC41⋊C5 ⋊ Dic3×C13
SylowC41 ⋊ C5×Dic3×C13
HallC3×C13 ⋊ Dic41⋊C5
SylowC3 ⋊ C13×Dic41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(D41⋊C5)
commutator, hypocenterC3×C41C4×C5×C13
FrattiniC2C13×C3⋊(D41⋊C5)
Fitting, socleC2×C3×C13×C41C2×C5
prime radicalC2×C3×C13×C41⋊C5C2
cosocleC2×C3×C41C2×C5×C13
LCSG ▷ C3×C41
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 24);