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C2×C3×C19⋊(D31⋊C5) #47977679

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

Aliases

direct productC2×C3×C19⋊(D31⋊C5)
unambiguous semidirect product(C2×C3×D589)⋊C5

Splittings

Fitting, socleC2×C3×C19×C31 ⋊ C2×C5
derived, HallC19×C31 ⋊ C22×C3×C5
HallC3×C19×ΓL(1,𝔽32) ⋊ C22
HallC2×C3×D589 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×D589 ⋊ C3×C5
HallC3×C19×C31 ⋊ C22×C5
HallC3×ΓL(1,𝔽32) ⋊ C2×D19
HallΓL(1,𝔽32) ⋊ C2×C3×D19
HallC3×C31 ⋊ C2×C5×D19
HallC3×C19 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C3×C5×D19
SylowC19 ⋊ C2×C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C19⋊(D31⋊C5)
commutator, cosocle, hypocenterC19×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C19×C31C2×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3534

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 151);