Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | Aut(G) order 6717312 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4998 |
| direct product | C2×D2499 |
| unambiguous semidirect product | (C2×C3)⋊D833 |
| unambiguous semidirect product | (C2×C17)⋊D147 |
| unambiguous semidirect product | (C2×C49)⋊D51 |
| Fitting | C2×C3×C17×C49 ⋊ C2 |
| derived, Hall | C3×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D51 |
| Sylow | C17 ⋊ C2×D147 |
| Sylow | C3 ⋊ C2×D833 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2499 |
| commutator, cosocle, hypocenter | C3×C17×C49 | C22 |
| Frattini | C7 | C2×D357 |
| Fitting | C2×C3×C17×C49 | C2 |
| socle | C2×C3×C7×C17 | D7 |
| LCS | G ▷ C3×C17×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
2502 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D7497, C2×C3⋊(C17⋊(D49⋊C3)), D3×D2499, … |
| maximal normal subgroup of | C2×C3⋊(C17⋊(D49⋊C3)), C2×C3×D2499, D9996 |
| maximal quotient of | C2×D7497, D3×D2499, C2×C3⋊D2499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 40);