Finite Group DatabasebetaFinite Group Databasebeta| order | 9843 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C193⋊C3 |
| unambiguous semidirect product | C193⋊(C3×C17) |
| unambiguous semidirect product | (C17×C193)⋊C3 |
| Fitting, socle, Hall | C17×C193 ⋊ C3 |
| derived, Sylow | C193 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C193⋊C3 |
| commutator, cosocle, hypocenter | C193 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C193 | C3 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
1139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C193⋊C3, C17×D193⋊C3, D17×C193⋊C3, … |
| maximal normal subgroup of | C2×C17×C193⋊C3, C17×D193⋊C3, D17×C193⋊C3, … |
| maximal quotient of | C2×C17×C193⋊C3, C17×C193⋊C9, C3×C17×C193⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9843, 1);