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C13⋊C3×AGL(1,𝔽23) #34089427

order19734
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C11×C13⋊C3)
unambiguous semidirect product(C23⋊C11)⋊(C2×C13⋊C3)
unambiguous semidirect product(C13⋊C3×D23)⋊C11
unambiguous semidirect product(C13×AGL(1,𝔽23))⋊C3

Splittings

Fitting, socle, derived, HallC13×C23 ⋊ C2×C3×C11
HallC13⋊C3×C23⋊C11 ⋊ C2
HallC13×AGL(1,𝔽23) ⋊ C3
HallC13×C23⋊C11 ⋊ C2×C3
HallC13⋊C3×D23 ⋊ C11
HallC23×C13⋊C3 ⋊ C2×C11
HallC13×D23 ⋊ C3×C11
HallC23⋊C11 ⋊ C2×C13⋊C3
HallD23 ⋊ C11×C13⋊C3
SylowC23 ⋊ C2×C11×C13⋊C3
SylowC13 ⋊ C3×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C23C2×C3×C11
LCSG ▷ C13×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 299

Conjugacy classes & character table

161 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 34);