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C19×C29×AGL(1,𝔽7) #37529034

order23142
automorphism?
homologyAbelianization (H1) = C2×C3×C19×C29 · Schur multiplier (H2) = C1

Aliases

direct productC19×C29×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C19×C29)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C19×C29)
unambiguous semidirect product(D7×C29)⋊(C3×C19)

Splittings

Fitting, socle, HallC7×C19×C29 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C19×C29
HallC19×ΓL(1,𝔽8)×C29 ⋊ C2
HallD7×C19×C29 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C19
HallD7×C29 ⋊ C3×C19
HallC19×ΓL(1,𝔽8) ⋊ C2×C29
HallD7×C19 ⋊ C3×C29
HallC7×C29 ⋊ C2×C3×C19
HallC7×C19 ⋊ C2×C3×C29
HallΓL(1,𝔽8) ⋊ C2×C19×C29
HallD7 ⋊ C3×C19×C29

Subgroups

subgroupG/H
center, hypercenterC19×C29AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C19×C29
FrattiniC1G
Fitting, socleC7×C19×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C19×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3857

Conjugacy classes & character table

3857 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 43);