Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×Dic17 |
| derived, Sylow | C17 ⋊ C3×C4×C72 |
| Hall | C3×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ C3×C4 |
| Hall | C3×C17 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | D17 |
| commutator, hypocenter | C17 | C3×C4×C72 |
| Frattini | C2 | C3×C72×D17 |
| Fitting, socle, prime radical | C2×C3×C72×C17 | C2 |
| cosocle | C2×C17 | C2×C3×C72 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C3×C72 | |
120 conjugacy classes of subgroups.
2940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C7⋊C9×Dic17, Dic17×#89204, Dic17×#89205, … |
| maximal normal subgroup of | C7×C7⋊C9×Dic17, Dic17×#89204, Dic17×#89205, … |
| maximal quotient of | C72×C9×Dic17, C3×C72×Dic51, C32×C72×Dic17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 64);