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C19×ΓL(1,𝔽8)⋊D29 #37529038

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

Aliases

direct productC19×ΓL(1,𝔽8)⋊D29
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×D29)
unambiguous semidirect productC29⋊(C19×AGL(1,𝔽7))
unambiguous semidirect productD203⋊(C3×C19)

Splittings

Fitting, socle, HallC7×C19×C29 ⋊ C2×C3
derived, HallC7×C29 ⋊ C2×C3×C19
HallC19×ΓL(1,𝔽8)×C29 ⋊ C2
HallC19×D203 ⋊ C3
HallΓL(1,𝔽8)×C29 ⋊ C2×C19
HallC19×C29 ⋊ AGL(1,𝔽7)
HallD203 ⋊ C3×C19
HallC19×ΓL(1,𝔽8) ⋊ D29
HallC7×C19 ⋊ C3×D29
SylowC29 ⋊ C19×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C19×D29
SylowC7 ⋊ C3×C19×D29

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)⋊D29
commutator, cosocle, hypocenterC7×C29C2×C3×C19
FrattiniC1G
Fitting, socleC7×C19×C29C2×C3
LCSG ▷ C7×C29
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3857

Conjugacy classes & character table

1463 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 47);