Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C59⋊AGL(1,𝔽13) |
| unambiguous semidirect product | (C59⋊#261)⋊C3 |
| Fitting, socle, derived, Hall | C13×C59 ⋊ C3×C4 |
| Hall | C59⋊#261 ⋊ C3 |
| Hall | C13⋊C3×C59 ⋊ C4 |
| Sylow | C59 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ Dic59 |
| Sylow | C13 ⋊ C3×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C59 | C3×C4 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13,59|a^2=c,d^a=d^5,e^a=e^58,d^b=d^3,d^c=d^12245 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C59⋊AGL(1,𝔽13), C3⋊(C59⋊AGL(1,𝔽13)) |
| maximal normal subgroup of | C3×C59⋊AGL(1,𝔽13) |
| maximal quotient of | C59⋊(#261⋊C9), C3×C59⋊AGL(1,𝔽13), C3⋊(C59⋊AGL(1,𝔽13)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 15);