Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2×C7 |
| direct product | C22×C17×#3862 |
| Fitting, socle, Hall | C22×C72×C17 ⋊ C3 |
| derived, Sylow | C72 ⋊ C22×C3×C17 |
| Hall | C72×C17 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C17 | #3862 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C17 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C17 | |
100 conjugacy classes of subgroups.
1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 172);