Finite Group Databasebeta

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C3×#24922536 #44544421

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

Aliases

direct productC3×#24922536

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ Dic5
HallC3×C5×C41 ⋊ Dic13
HallC13×C41 ⋊ C3×Dic5
HallC5×C41 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ #4223
HallC3×C41 ⋊ Dic65
HallC5×C13 ⋊ C3×#4223
SylowC41 ⋊ C3×Dic65
HallC3×C13 ⋊ #11717964
HallC3×C5 ⋊ #14523824
SylowC13 ⋊ C3×#11717964
SylowC5 ⋊ C3×#14523824

Subgroups

subgroupG/H
center, hypercenterC3#24922536
commutator, hypocenterC5×C13×C41C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×C5×C13×D41C2
cosocleC5×C13×D41C2×C3
LCSG ▷ C5×C13×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 149);