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C13×ΓL(1,𝔽8)⋊(D19⋊C3) #44527655

order31122
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×ΓL(1,𝔽8)⋊(D19⋊C3)
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C13×AGL(1,𝔽7))
unambiguous semidirect product((C19⋊C3)⋊D7)⋊(C3×C13)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D19)⋊(C3×C13)
unambiguous semidirect product#11716327⋊(C3×C13)
unambiguous semidirect product#11716328⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C32
derived, HallC7×C19 ⋊ C2×C32×C13
HallC13×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2
HallC13×D133 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C2×C13
HallD133 ⋊ C32×C13
HallC13×C19 ⋊ C3×AGL(1,𝔽7)
HallC7×C13 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×C13×AGL(1,𝔽7)
SylowC7 ⋊ C3×C13×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)⋊(D19⋊C3)
commutator, cosocle, hypocenterC7×C19C2×C32×C13
FrattiniC1G
Fitting, socleC7×C13×C19C2×C32
LCSG ▷ C7×C19
UCSC1 ◁ C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 138);