Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28570268160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C32×C9 |
| abelian | C24×C3×C9×C27 |
| multiplicative | (ℤ/43092)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C9 | C24×C33 |
| socle, prime radical | C24×C33 | C3×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
13534 conjugacy classes of subgroups.
11664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×C3×C4×C9×C27, C25×C3×C9×C27 |
| maximal normal subgroup of | C23×C3×C4×C9×C27, C25×C3×C9×C27 |
| maximal quotient of | C23×C3×C4×C9×C27, C25×C3×C9×C27 |
Past the SmallGroups library coverage — no SmallGroups id.