Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of #64424 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×#64424 |
| Fitting, socle | C2×C72×C17 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C17 |
| Hall | C2×C17×C7⋊D7 ⋊ C3 |
| Hall | C17×#3861 ⋊ C22 |
| Hall | C72×C17 ⋊ C22×C3 |
| Hall | C2×C7⋊D7 ⋊ C3×C17 |
| Hall | #3861 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | #64424 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C17 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C17 | |
200 conjugacy classes of subgroups.
476 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 117);