Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×AGL(1,𝔽13) |
| unambiguous semidirect product | #261⋊(C3×C59) |
| unambiguous semidirect product | (#261×C59)⋊C3 |
| Fitting, socle, Hall | C13×C59 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C3×C4×C59 |
| Hall | #261×C59 ⋊ C3 |
| Hall | C13⋊C3×C59 ⋊ C4 |
| Hall | #261 ⋊ C3×C59 |
| Hall | C13⋊C3 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C3×C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C13×C59 | C3×C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C59 | |
24 conjugacy classes of subgroups.
767 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C59×AGL(1,𝔽13), C59×C3⋊AGL(1,𝔽13) |
| maximal normal subgroup of | C3×C59×AGL(1,𝔽13) |
| maximal quotient of | C59×#261⋊C9, C3×C59×AGL(1,𝔽13), C59×C3⋊AGL(1,𝔽13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 14);