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C13⋊C3×ΓL(1,𝔽8)⋊D23 #49179170

order37674
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×ΓL(1,𝔽8)⋊D23
unambiguous semidirect productΓL(1,𝔽8)⋊(C13⋊C3×D23)
unambiguous semidirect productC23⋊(C13⋊C3×AGL(1,𝔽7))
unambiguous semidirect product(C13⋊C3×D161)⋊C3
unambiguous semidirect product(C13×ΓL(1,𝔽8)⋊D23)⋊C3
unambiguous semidirect product(C23⋊#10587720)⋊C3
unambiguous semidirect product(C23⋊#10587721)⋊C3

Splittings

Fitting, socle, derived, HallC7×C13×C23 ⋊ C2×C32
HallΓL(1,𝔽8)×C23×C13⋊C3 ⋊ C2
HallC13×D161 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ D23
HallD161 ⋊ C3×C13⋊C3
HallC13×C23 ⋊ C3×AGL(1,𝔽7)
HallC7×C23 ⋊ C2×C3×C13⋊C3
HallC7×C13 ⋊ C32×D23
SylowC23 ⋊ C13⋊C3×AGL(1,𝔽7)
SylowC13 ⋊ C3×ΓL(1,𝔽8)⋊D23
SylowC7 ⋊ C3×C13⋊C3×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C23C2×C32
LCSG ▷ C7×C13×C23
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 53);