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C41×Dic65⋊C3 #44544304

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C41)
unambiguous semidirect product(C41×Dic65)⋊C3

Splittings

derived, HallC5×C13 ⋊ C3×C4×C41
HallC41×Dic65 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC5×C13×C41 ⋊ C3×C4
HallC13⋊C3×C41 ⋊ Dic5
HallC13×C41 ⋊ C3×Dic5
HallDic65 ⋊ C3×C41
HallC5×C41 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C4×C41
HallC13⋊C3 ⋊ Dic5×C41
SylowC13 ⋊ C3×Dic5×C41
SylowC5 ⋊ C41×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C41C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C41
FrattiniC2C41×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C13×C41C2×C3
prime radicalC2×C5×C13⋊C3×C41C2
cosocleC2×C5×C13C2×C3×C41
LCSG ▷ C5×C13
UCSC1 ◁ C2×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10660

Conjugacy classes & character table

1804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 32);