Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D357 |
| unambiguous semidirect product | (C3×D7)⋊D119 |
| unambiguous semidirect product | (C7×D7)⋊D51 |
| unambiguous semidirect product | (D7×C17)⋊D21 |
| Fitting, socle, derived, Hall | C3×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ D72 |
| Sylow | C72 ⋊ C2×D51 |
| Sylow | C17 ⋊ D7×D21 |
| Sylow | C3 ⋊ D7×D119 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C17 | C22 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D1071, #64418⋊D51, D7×C3⋊(C17⋊AGL(1,𝔽7)), … |
| maximal normal subgroup of | D7×C3⋊(C17⋊AGL(1,𝔽7)), AGL(1,𝔽7)×D357, #64423⋊D51, … |
| maximal quotient of | D7×D1071, C3×D7×D357, D21×D357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 159);