Finite Group DatabasebetaFinite Group Databasebeta| order | 9894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D97⋊C3 |
| unambiguous semidirect product | D97⋊(C3×C17) |
| unambiguous semidirect product | (C97⋊C3)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D97)⋊C3 |
| Fitting, socle, Hall | C17×C97 ⋊ C2×C3 |
| derived, Sylow | C97 ⋊ C2×C3×C17 |
| Hall | C17×C97⋊C3 ⋊ C2 |
| Hall | C17×D97 ⋊ C3 |
| Hall | C97⋊C3 ⋊ C2×C17 |
| Hall | D97 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C97 | C2×C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
374 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#87604⋊C3, #20268666⋊C3, D17×D97⋊C3, … |
| maximal normal subgroup of | C17×#87604⋊C3, #20268666⋊C3, D17×D97⋊C3, … |
| maximal quotient of | C17×Dic97⋊C3, C2×C17×D97⋊C3, C17×D97⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9894, 10);