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C2×(C19⋊C3)⋊(D31⋊C5) #47977611

order35340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C19⋊C3)⋊(D31⋊C5)
unambiguous semidirect product(C2×C19⋊C3)⋊(D31⋊C5)
unambiguous semidirect product(C2×(C19⋊C3)⋊D31)⋊C5

Splittings

Fitting, socleC2×C19×C31 ⋊ C2×C3×C5
derived, HallC19×C31 ⋊ C22×C3×C5
HallC2×C19⋊(D31⋊C5) ⋊ C3
HallC19⋊C3×ΓL(1,𝔽32) ⋊ C22
HallC2×(C19⋊C3)⋊D31 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×D589 ⋊ C3×C5
HallC31×C19⋊C3 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C2×C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2(C19⋊C3)⋊(D31⋊C5)
commutator, cosocle, hypocenterC19×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1178

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 83);