Finite Group DatabasebetaFinite Group Databasebeta| order | 10998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D47×C13⋊C9 |
| unambiguous semidirect product | C47⋊(C2×C13⋊C9) |
| unambiguous semidirect product | (C13×D47)⋊C9 |
| derived, Hall | C13×C47 ⋊ C2×C9 |
| Hall | C47×C13⋊C9 ⋊ C2 |
| Hall | C13×D47 ⋊ C9 |
| Sylow | C47 ⋊ C2×C13⋊C9 |
| Sylow | C13 ⋊ C9×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C13⋊C3×D47 |
| commutator, hypocenter | C13×C47 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C47 | C2×C3 |
| prime radical | C3×C13×D47 | C3 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
525 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D13⋊C9, C2×D47×C13⋊C9 |
| maximal normal subgroup of | D47×D13⋊C9, C2×D47×C13⋊C9 |
| maximal quotient of | C13⋊C9×Dic47, C2×D47×C13⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10998, 10);