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C43×ΓL(1,𝔽8)⋊D13 #37553522

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×ΓL(1,𝔽8)⋊D13
unambiguous semidirect productΓL(1,𝔽8)⋊(D13×C43)

Splittings

Fitting, socle, HallC7×C13×C43 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C43
HallC13×ΓL(1,𝔽8)×C43 ⋊ C2
HallC43×D91 ⋊ C3
HallΓL(1,𝔽8)×C43 ⋊ D13
HallC13×C43 ⋊ AGL(1,𝔽7)
HallC7×C43 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ C2×C43
HallD91 ⋊ C3×C43
HallΓL(1,𝔽8) ⋊ D13×C43
SylowC13 ⋊ AGL(1,𝔽7)×C43
SylowC7 ⋊ C3×D13×C43

Subgroups

subgroupG/H
center, hypercenterC43ΓL(1,𝔽8)⋊D13
commutator, cosocle, hypocenterC7×C13C2×C3×C43
FrattiniC1G
Fitting, socleC7×C13×C43C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3913

Conjugacy classes & character table

1591 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 111);