Finite Group DatabasebetaFinite Group Databasebeta| order | 29232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 193536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C7×C9×C29 |
| multiplicative | (ℤ/32509)ˣ, (ℤ/37465)ˣ, (ℤ/45501)ˣ, (ℤ/46197)ˣ, (ℤ/47937)ˣ, (ℤ/58472)ˣ, (ℤ/60668)ˣ, (ℤ/63916)ˣ, (ℤ/65018)ˣ, (ℤ/74930)ˣ, (ℤ/87708)ˣ, (ℤ/90828)ˣ, (ℤ/91002)ˣ, (ℤ/92394)ˣ, (ℤ/95874)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C7×C29 |
| socle, prime radical | C23×C3×C7×C29 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
29232 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.