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C3×(C13⋊C3)⋊(D31⋊C5) #49136563

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C13⋊C3)⋊(D31⋊C5)
unambiguous semidirect product(C13⋊C3)⋊(C3×D31⋊C5)
unambiguous semidirect product(C3×(C13⋊C3)⋊D31)⋊C5

Splittings

Fitting, socleC3×C13×C31 ⋊ C2×C3×C5
derived, HallC13×C31 ⋊ C2×C32×C5
HallC3×C13⋊C3×ΓL(1,𝔽32) ⋊ C2
HallC3×(C13⋊C3)⋊D31 ⋊ C5
HallC13⋊(D31⋊C5) ⋊ C32
HallC3×C31×C13⋊C3 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallD403 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×D13⋊C3
HallC3×C13⋊C3 ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×D13⋊C3
SylowC13 ⋊ C32×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊(D31⋊C5)
commutator, cosocle, hypocenterC13×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 83);