Finite Group Databasebeta

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C5×C13⋊C3×#4223 #44544348

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

Aliases

direct productC5×C13⋊C3×#4223
unambiguous semidirect product(C5×C13×#4223)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C3×C4
derived, HallC13×C41 ⋊ C3×C4×C5
HallC5×C13×#4223 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC13×#4223 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC5×C41 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×#4223
SylowC41 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×#4223

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×#4223
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C41C3×C4
prime radicalC5×C13⋊C3×D41C2
cosocleC13×D41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 76);