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C13×C3⋊AGL(1,𝔽23) #34089417

order19734
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊AGL(1,𝔽23)
unambiguous semidirect productC3⋊(C13×AGL(1,𝔽23))
unambiguous semidirect productD69⋊(C11×C13)
unambiguous semidirect product(C23⋊C11)⋊(D3×C13)
unambiguous semidirect product(C13×D69)⋊C11

Splittings

Fitting, socle, HallC3×C13×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C2×C11×C13
HallC3×C13×C23⋊C11 ⋊ C2
HallC13×C23⋊C11 ⋊ D3
HallC13×D69 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C13
HallC13×C23 ⋊ D3×C11
HallC23⋊C11 ⋊ D3×C13
HallD69 ⋊ C11×C13
HallC3×C13 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ D3×C11×C13
SylowC3 ⋊ C13×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC13C3⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC3×C23C2×C11×C13
FrattiniC1G
Fitting, socleC3×C13×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 897

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 24);