Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C3⋊(C7⋊D119) |
| unambiguous semidirect product | (C2×C3)⋊(C7⋊D119) |
| unambiguous semidirect product | (C2×C7)⋊D357 |
| unambiguous semidirect product | (C2×C17)⋊(C3⋊(C7⋊D7)) |
| Fitting, socle | C2×C3×C72×C17 ⋊ C2 |
| derived, Hall | C3×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D51 |
| Sylow | C17 ⋊ C2×C3⋊(C7⋊D7) |
| Sylow | C3 ⋊ C2×C7⋊D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C7⋊D119) |
| commutator, cosocle, hypocenter | C3×C72×C17 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72×C17 | C2 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 ◁ C2 | |
200 conjugacy classes of subgroups.
2502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 175);