Finite Group DatabasebetaFinite Group Databasebeta| order | 3267 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C5×C9×C11 (order 1980) · Inn(G) = C1 · Out(G) = C22×C5×C9×C11 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C3267 |
| abelian | C27×C121 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9×C11 | C3×C11 |
| socle, prime radical | C3×C11 | C9×C11 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
3267 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C27×C121, C81×C121, C3×C27×C121, … |
| maximal normal subgroup of | C2×C27×C121, C81×C121, C3×C27×C121, … |
| maximal quotient of | C2×C27×C121, C81×C121, C3×C27×C121, … |
Past the SmallGroups library coverage — no SmallGroups id.