Finite Group DatabasebetaFinite Group Databasebeta| order | 17898 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#22582162 |
| Fitting, socle, Hall | C2×C19×C157 ⋊ C3 |
| derived, Hall | C19×C157 ⋊ C2×C3 |
| Hall | C2×C157 ⋊ C19⋊C3 |
| Sylow | C157 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ C157⋊C3 |
| Sylow | C19 ⋊ C2×C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22582162 |
| commutator, cosocle, hypocenter | C19×C157 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C157 | C3 |
| LCS | G ▷ C19×C157 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5966 |
1994 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22582162, #49088896, #49088900, … |
| maximal normal subgroup of | C4×#22582162, #49088896, #49088900, … |
| maximal quotient of | C4×#22582162, C22×#22582162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17898, 5);