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(C13⋊C3)⋊AGL(1,𝔽23) #34089429

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

Aliases

unambiguous semidirect product(C13⋊C3)⋊AGL(1,𝔽23)
unambiguous semidirect product(C23⋊C11)⋊(D13⋊C3)
unambiguous semidirect product(C23⋊(D13⋊C3))⋊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
HallC23⋊(D13⋊C3) ⋊ C11
HallC23×C13⋊C3 ⋊ C2×C11
HallD299 ⋊ C3×C11
HallC23⋊C11 ⋊ D13⋊C3
HallC13⋊C3 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C11×D13⋊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

Polycyclic presentation:

2,3,11,13,23|d^a=d^12,e^a=e^22,d^b=d^3,e^c=e^2

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 36);