Finite Group DatabasebetaFinite Group Databasebeta| order | 10818 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C601⋊C9 |
| unambiguous semidirect product | (C2×C601)⋊C9 |
| derived, Sylow | C601 ⋊ C2×C9 |
| Hall | C2×C601 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C601⋊C3 |
| commutator, hypocenter | C601 | C2×C9 |
| Frattini | C3 | C2×C601⋊C3 |
| Fitting, socle, prime radical | C2×C3×C601 | C3 |
| cosocle | C3×C601 | C2×C3 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
1218 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic601⋊C9, C4×C601⋊C9, C2×D601⋊C9, … |
| maximal normal subgroup of | Dic601⋊C9, C4×C601⋊C9, C2×D601⋊C9, … |
| maximal quotient of | C4×C601⋊C9, C22×C601⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10818, 3);