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C13×ΓL(1,𝔽8)⋊D59 #44567284

order32214
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)⋊D59
unambiguous semidirect productΓL(1,𝔽8)⋊(C13×D59)
unambiguous semidirect productC59⋊(C13×AGL(1,𝔽7))
unambiguous semidirect productD413⋊(C3×C13)

Splittings

Fitting, socle, HallC7×C13×C59 ⋊ C2×C3
derived, HallC7×C59 ⋊ C2×C3×C13
HallC13×ΓL(1,𝔽8)×C59 ⋊ C2
HallC13×D413 ⋊ C3
HallΓL(1,𝔽8)×C59 ⋊ C2×C13
HallD413 ⋊ C3×C13
HallC13×C59 ⋊ AGL(1,𝔽7)
HallC13×ΓL(1,𝔽8) ⋊ D59
HallC7×C13 ⋊ C3×D59
SylowC59 ⋊ C13×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C13×D59
SylowC7 ⋊ C3×C13×D59

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)⋊D59
commutator, cosocle, hypocenterC7×C59C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C59C2×C3
LCSG ▷ C7×C59
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5369

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 38);