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C2×C13⋊C3×C41⋊C5 #30630516

order15990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13⋊C3×C41⋊C5
unambiguous semidirect product(C2×C13)⋊(C3×C41⋊C5)
unambiguous semidirect product(C2×C41)⋊(C5×C13⋊C3)
unambiguous semidirect product(C2×C13⋊C3×C41)⋊C5
unambiguous semidirect product(C2×C13×C41⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C13×C41 ⋊ C3×C5
derived, HallC13×C41 ⋊ C2×C3×C5
HallC2×C13×C41⋊C5 ⋊ C3
HallC2×C13⋊C3×C41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×C3
HallC13⋊C3×C41 ⋊ C2×C5
HallC2×C41 ⋊ C5×C13⋊C3
SylowC41 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ C3×C41⋊C5
SylowC13 ⋊ C2×C3×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C41⋊C5
commutator, cosocle, hypocenterC13×C41C2×C3×C5
FrattiniC1G
Fitting, socleC2×C13×C41C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1066

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C13⋊C3×C41⋊C5, C13⋊C3×Dic41⋊C5, Dic13⋊C3×C41⋊C5, …
maximal normal subgroup ofC4×C13⋊C3×C41⋊C5, C13⋊C3×Dic41⋊C5, Dic13⋊C3×C41⋊C5, …
maximal quotient ofC4×C13⋊C3×C41⋊C5, C22×C13⋊C3×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 4);