Finite Group DatabasebetaFinite Group Databasebeta| order | 6708 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C43×#261) |
| Fitting, socle, Hall | C3×C13×C43 ⋊ C4 |
| derived, Hall | C3×C13 ⋊ C4×C43 |
| Hall | C13×C43 ⋊ Dic3 |
| Hall | C3×C43 ⋊ #261 |
| Sylow | C13 ⋊ Dic3×C43 |
| Sylow | C3 ⋊ C43×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C43 | C4 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C43 | |
24 conjugacy classes of subgroups.
645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6708, 54);