Finite Group Databasebeta

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C5×C41×C3⋊#261 #44544429

order31980
automorphism?
homologyAbelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41×C3⋊#261
unambiguous semidirect productC3⋊(C5×C41×#261)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC3×C13 ⋊ C4×C5×C41
HallC5×C13×C41 ⋊ Dic3
HallC3×C13×C41 ⋊ C4×C5
HallC3×C5×C41 ⋊ #261
HallC13×C41 ⋊ C5×Dic3
HallC3×C5×C13 ⋊ C4×C41
HallC3×C41 ⋊ C5×#261
HallC5×C13 ⋊ Dic3×C41
HallC3×C5 ⋊ C41×#261
SylowC13 ⋊ C5×Dic3×C41
SylowC3 ⋊ C5×C41×#261

Subgroups

subgroupG/H
center, hypercenterC5×C41C3⋊#261
commutator, hypocenterC3×C13C4×C5×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C5×D13×C41C2
cosocleC3×D13C2×C5×C41
LCSG ▷ C3×C13
UCSC1 ◁ C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

3075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 157);