Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C4×C17×#3861 |
| Fitting, Hall | C4×C72×C17 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C4×C17 |
| Hall | C72×C17 ⋊ C3×C4 |
| Hall | C4×C72 ⋊ C3×C17 |
120 conjugacy classes of subgroups.
1292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C17×ΓL(1,𝔽8)2, Dic3×C17×#3861, C3×C4×C17×#3861 |
| maximal normal subgroup of | C4×C17×ΓL(1,𝔽8)2, C3×C4×C17×#3861 |
| maximal quotient of | C4×C17×#89204, Dic3×C17×#3861, C3×C4×C17×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 62);