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C3×C13×D41⋊C5 #30630532

order15990
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D41⋊C5
unambiguous semidirect productD41⋊(C3×C5×C13)
unambiguous semidirect product(C41⋊C5)⋊(C2×C3×C13)
unambiguous semidirect product(C3×D41)⋊(C5×C13)
unambiguous semidirect product(C3×C13×D41)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C2×C3×C5×C13
HallC3×C13×C41⋊C5 ⋊ C2
HallC3×C13×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×C3
HallC13×D41 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ C2×C13
HallC13×C41 ⋊ C2×C3×C5
HallC3×D41 ⋊ C5×C13
HallC41⋊C5 ⋊ C2×C3×C13
HallC3×C41 ⋊ C2×C5×C13
HallD41 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13D41⋊C5
commutator, cosocle, hypocenterC41C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C13×#4223⋊C5, C3×#14523824⋊C5, C3×D13×D41⋊C5, …
maximal normal subgroup ofC3×C13×#4223⋊C5, C3×#14523824⋊C5, C3×D13×D41⋊C5, …
maximal quotient ofC3×C13×Dic41⋊C5, C2×C3×C13×D41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 20);