Finite Group DatabasebetaFinite Group Databasebeta| order | 9317 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C5×C121 (order 7260) · Inn(G) = C1 · Out(G) = C22×C3×C5×C121 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C9317 |
| abelian | C7×C1331 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C121 | C7×C11 |
| socle, prime radical | C7×C11 | C121 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8 conjugacy classes of subgroups.
9317 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic9317, C2×D9317 |
| maximal subgroup of | C2×C7×C1331, C3×C7×C1331, D9317 |
| maximal normal subgroup of | C2×C7×C1331, C3×C7×C1331, D9317 |
| maximal quotient of | C2×C7×C1331, C3×C7×C1331 |
Past the SmallGroups library coverage — no SmallGroups id.