Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×#6157 |
| Fitting, socle, Hall | C3×C11×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C3×C4×C11 |
| Hall | C11×C53 ⋊ C3×C4 |
| Hall | C3×C53 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | #6157 |
| commutator, hypocenter | C53 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C53 | C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
561 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 10);