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Dic39×C41⋊C5 #44544297

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

Aliases

direct productDic39×C41⋊C5
unambiguous semidirect productC3⋊(Dic13×C41⋊C5)
unambiguous semidirect product(C41×Dic39)⋊C5

Splittings

derived, HallC3×C13×C41 ⋊ C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC41×Dic39 ⋊ C5
HallC13×C41⋊C5 ⋊ Dic3
HallC3×C41⋊C5 ⋊ Dic13
HallC13×C41 ⋊ C5×Dic3
HallC3×C41 ⋊ C5×Dic13
SylowC41 ⋊ C5×Dic39
HallC3×C13 ⋊ C4×C41⋊C5
SylowC13 ⋊ Dic3×C41⋊C5
SylowC3 ⋊ Dic13×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D39×C41⋊C5
commutator, hypocenterC3×C13×C41C4×C5
Fitting, socle, cosocleC2×C3×C13×C41C2×C5
prime radicalC2×C3×C13×C41⋊C5C2
LCSG ▷ C3×C13×C41
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 25);