Finite Group Databasebeta

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C3×C5×#14523823 #44544396

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#14523823

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC13×C41 ⋊ C3×C4×C5
HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ C4×C5
HallC3×C5×C41 ⋊ #261
HallC5×C41 ⋊ C3×#261
HallC3×C5×C13 ⋊ Dic41
HallC3×C41 ⋊ C5×#261
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C3×C5×#261
HallC3×C13 ⋊ C5×Dic41
SylowC13 ⋊ C3×C5×Dic41

Subgroups

subgroupG/H
center, hypercenterC3×C5#14523823
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C5×D13×C41C2
cosocleD13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 124);