Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 687150786894888960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C410 |
| abelian | C2×C3×C45 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C26×C3 |
| socle, prime radical | C26×C3 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1061328 conjugacy classes of subgroups.
6144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C44×C8, C3×C46, C22×C3×C45, … |
| maximal normal subgroup of | C2×C3×C44×C8, C3×C46, C22×C3×C45, … |
| maximal quotient of | C2×C3×C44×C8, C3×C46, C22×C3×C45, … |
Past the SmallGroups library coverage — no SmallGroups id.