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C13×C3⋊(D41⋊C5) #30630536

order15990
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(D41⋊C5)
unambiguous semidirect productC3⋊(C13×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(D3×C13)
unambiguous semidirect productD123⋊(C5×C13)
unambiguous semidirect product(C13×D123)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C2×C5
derived, HallC3×C41 ⋊ C2×C5×C13
HallC3×C13×C41⋊C5 ⋊ C2
HallC13×D123 ⋊ C5
HallC13×C41⋊C5 ⋊ D3
HallC3×C41⋊C5 ⋊ C2×C13
HallC13×C41 ⋊ C5×D3
HallD123 ⋊ C5×C13
HallC41⋊C5 ⋊ D3×C13
SylowC41 ⋊ C5×D3×C13
HallC3×C13 ⋊ D41⋊C5
SylowC3 ⋊ C13×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(D41⋊C5)
commutator, cosocle, hypocenterC3×C41C2×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C13×D41⋊C5, D13×C3⋊(D41⋊C5), D39⋊(D41⋊C5), …
maximal normal subgroup ofD3×C13×D41⋊C5, D13×C3⋊(D41⋊C5), D39⋊(D41⋊C5), …
maximal quotient ofC13×C3⋊(Dic41⋊C5), C2×C13×C3⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 24);