Finite Group DatabasebetaFinite Group Databasebeta| order | 20298 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D199⋊C3 |
| unambiguous semidirect product | D199⋊(C3×C17) |
| unambiguous semidirect product | (C199⋊C3)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D199)⋊C3 |
| Fitting, socle, Hall | C17×C199 ⋊ C2×C3 |
| derived, Sylow | C199 ⋊ C2×C3×C17 |
| Hall | C17×C199⋊C3 ⋊ C2 |
| Hall | C17×D199 ⋊ C3 |
| Hall | C199⋊C3 ⋊ C2×C17 |
| Hall | D199 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D199⋊C3 |
| commutator, cosocle, hypocenter | C199 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C199 | C2×C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3383 |
663 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20298, 10);