Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 786432 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C16 |
| abelian | C2×C3×C162 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C82 | C23×C3 |
| socle, prime radical | C23×C3 | C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
644 conjugacy classes of subgroups.
1536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C16×C32, C3×C4×C162, C22×C3×C162, … |
| maximal normal subgroup of | C2×C3×C16×C32, C3×C4×C162, C22×C3×C162, … |
| maximal quotient of | C2×C3×C16×C32, C3×C4×C162, C22×C3×C162, … |
Past the SmallGroups library coverage — no SmallGroups id.