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C3×C13⋊AGL(1,𝔽23) #34089415

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

Aliases

direct productC3×C13⋊AGL(1,𝔽23)
unambiguous semidirect product(C23⋊C11)⋊(C3×D13)
unambiguous semidirect product(C3×D299)⋊C11

Splittings

Fitting, socle, HallC3×C13×C23 ⋊ C2×C11
derived, HallC13×C23 ⋊ C2×C3×C11
HallC3×C13×C23⋊C11 ⋊ C2
HallC13×C23⋊C11 ⋊ C2×C3
HallC3×D299 ⋊ C11
HallC3×C23⋊C11 ⋊ D13
HallD299 ⋊ C3×C11
HallC23⋊C11 ⋊ C3×D13
HallC3×C23 ⋊ C11×D13
HallC3×C13 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C3×C11×D13
SylowC13 ⋊ C3×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC3C13⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC13×C23C2×C3×C11
FrattiniC1G
Fitting, socleC3×C13×C23C2×C11
LCSG ▷ C13×C23
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 897

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 22);