Finite Group DatabasebetaFinite Group Databasebeta| order | 13134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×(C199⋊C3)⋊C11 |
| unambiguous semidirect product | (C2×C199⋊C3)⋊C11 |
| unambiguous semidirect product | (C2×C199⋊C11)⋊C3 |
| Fitting, socle, Hall | C2×C199 ⋊ C3×C11 |
| derived, Sylow | C199 ⋊ C2×C3×C11 |
| Hall | C2×C199⋊C11 ⋊ C3 |
| Hall | C199⋊C11 ⋊ C2×C3 |
| Hall | C2×C199⋊C3 ⋊ C11 |
| Hall | C199⋊C3 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C199⋊C3)⋊C11 |
| commutator, cosocle, hypocenter | C199 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C199 | C3×C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13134, 4);