Finite Group DatabasebetaFinite Group Databasebeta| order | 7992 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 31104 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C9×C37 |
| multiplicative | (ℤ/8251)ˣ, (ℤ/9583)ˣ, (ℤ/12321)ˣ, (ℤ/16502)ˣ, (ℤ/19166)ˣ, (ℤ/24642)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C37 |
| socle, prime radical | C22×C32×C37 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
160 conjugacy classes of subgroups.
7992 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.