Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C729 |
| multiplicative | (ℤ/7295)ˣ, (ℤ/8751)ˣ, (ℤ/10935)ˣ, (ℤ/11668)ˣ, (ℤ/14590)ˣ, (ℤ/17502)ˣ, (ℤ/21870)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C243 | C22×C3 |
| socle, prime radical | C22×C3 | C2×C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
56 conjugacy classes of subgroups.
5832 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.