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C5×C13⋊C3×Dic41 #44544299

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

Aliases

direct productC5×C13⋊C3×Dic41
unambiguous semidirect product(C5×C13×Dic41)⋊C3

Splittings

derived, HallC13×C41 ⋊ C3×C4×C5
HallC5×C13×Dic41 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC5×C13×C41 ⋊ C3×C4
HallC13×Dic41 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC5×C41 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×D41
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC2C5×C13⋊C3×D41
Fitting, socleC2×C5×C13×C41C2×C3
prime radicalC2×C5×C13⋊C3×C41C2
cosocleC2×C13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10660

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 27);