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C13×D615 #30630529

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

Aliases

direct productC13×D615
unambiguous semidirect productC3⋊(C13×D205)
unambiguous semidirect productC5⋊(C13×D123)
unambiguous semidirect productC41⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C2
derived, HallC3×C5×C41 ⋊ C2×C13
HallC5×C13×C41 ⋊ D3
HallC3×C13×C41 ⋊ D5
HallC13×C41 ⋊ D15
HallC5×C41 ⋊ D3×C13
HallC3×C5×C13 ⋊ D41
HallC3×C41 ⋊ D5×C13
HallC5×C13 ⋊ D123
SylowC41 ⋊ C13×D15
HallC3×C13 ⋊ D205
HallC3×C5 ⋊ C13×D41
SylowC5 ⋊ C13×D123
SylowC3 ⋊ C13×D205

Subgroups

subgroupG/H
center, hypercenterC13D615
commutator, cosocle, hypocenterC3×C5×C41C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C41C2
LCSG ▷ C3×C5×C41
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4017 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D15×D41, D13×D615, D533⋊D15, …
maximal normal subgroup ofC13×D15×D41, D13×D615, D533⋊D15, …
maximal quotient ofC13×Dic615, C2×C13×D615

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 17);