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C19×ΓL(1,𝔽8)⋊(D13⋊C3) #44527669

order31122
automorphism?
homologyAbelianization (H1) = C2×C32×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×ΓL(1,𝔽8)⋊(D13⋊C3)
unambiguous semidirect productΓL(1,𝔽8)⋊(C19×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C19×AGL(1,𝔽7))
unambiguous semidirect product((C13⋊C3)⋊D7)⋊(C3×C19)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊(C3×C19)
unambiguous semidirect product#10587722⋊(C3×C19)
unambiguous semidirect product#10587723⋊(C3×C19)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C32
derived, HallC7×C13 ⋊ C2×C32×C19
HallC19×ΓL(1,𝔽8)×C13⋊C3 ⋊ C2
HallC19×D91 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C2×C19
HallC13×C19 ⋊ C3×AGL(1,𝔽7)
HallD91 ⋊ C32×C19
HallC7×C19 ⋊ C3×D13⋊C3
SylowC13 ⋊ C3×C19×AGL(1,𝔽7)
SylowC7 ⋊ C3×C19×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC19ΓL(1,𝔽8)⋊(D13⋊C3)
commutator, cosocle, hypocenterC7×C13C2×C32×C19
FrattiniC1G
Fitting, socleC7×C13×C19C2×C32
LCSG ▷ C7×C13
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 152);