Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C53 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C11×C53 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C11×C53 |
| Hall | C22×C53 ⋊ C3×C11 |
| Hall | C22×C11 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C53 | A4 |
| commutator, hypocenter | C22 | C3×C11×C53 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C53 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C11×C53 | |
20 conjugacy classes of subgroups.
2332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×A4×C53, A4×C53×C11⋊C5, C5×C11×A4×C53, … |
| maximal normal subgroup of | C3×C11×A4×C53, A4×C53×C11⋊C5, C5×C11×A4×C53 |
| maximal quotient of | C11×C22⋊C9×C53, C3×C11×A4×C53, C5×C11×A4×C53 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 21);