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Dic3×C13×C41⋊C5 #44544295

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

Aliases

direct productDic3×C13×C41⋊C5
unambiguous semidirect productC3⋊(C4×C13×C41⋊C5)
unambiguous semidirect product(Dic3×C41)⋊(C5×C13)
unambiguous semidirect product(Dic3×C13×C41)⋊C5

Splittings

derived, HallC3×C41 ⋊ C4×C5×C13
HallC3×C13×C41⋊C5 ⋊ C4
HallDic3×C13×C41 ⋊ C5
HallC3×C13×C41 ⋊ C4×C5
HallC3×C41⋊C5 ⋊ C4×C13
HallC13×C41 ⋊ C5×Dic3
HallDic3×C41 ⋊ C5×C13
SylowC41 ⋊ C5×Dic3×C13
HallC3×C13 ⋊ C4×C41⋊C5
SylowC3 ⋊ C4×C13×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13D3×C41⋊C5
commutator, hypocenterC3×C41C4×C5×C13
FrattiniC2D3×C13×C41⋊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

1014 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 23);