Finite Group DatabasebetaFinite Group Databasebeta| order | 6912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 142690222080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C46 |
| abelian | C3×C44×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C24×C3 | C24×C32 |
| socle, prime radical | C24×C32 | C24×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
19830 conjugacy classes of subgroups.
6912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C43×C8×C9, C2×C3×C44×C9, C3×C44×C27, … |
| maximal normal subgroup of | C3×C43×C8×C9, C2×C3×C44×C9, C3×C44×C27, … |
| maximal quotient of | C3×C43×C8×C9, C2×C3×C44×C9, C3×C44×C27, … |
Past the SmallGroups library coverage — no SmallGroups id.