Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6288482304 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C36×C4 |
| abelian | C33×C4×C8×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4 | C22×C34 |
| socle, prime radical | C22×C34 | C2×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8712 conjugacy classes of subgroups.
7776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C33×C4×C9×C16, C33×C82×C9, C2×C33×C4×C8×C9, … |
| maximal normal subgroup of | C33×C4×C9×C16, C33×C82×C9, C2×C33×C4×C8×C9, … |
| maximal quotient of | C33×C4×C9×C16, C33×C82×C9, C2×C33×C4×C8×C9, … |
Past the SmallGroups library coverage — no SmallGroups id.