Finite Group DatabasebetaFinite Group Databasebeta| order | 29376 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1327104 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C9×C16×C17 |
| multiplicative | (ℤ/33269)ˣ, (ℤ/36533)ˣ, (ℤ/38437)ˣ, (ℤ/46971)ˣ, (ℤ/47277)ˣ, (ℤ/49419)ˣ, (ℤ/54621)ˣ, (ℤ/66538)ˣ, (ℤ/73066)ˣ, (ℤ/76874)ˣ, (ℤ/93942)ˣ, (ℤ/94554)ˣ, (ℤ/98838)ˣ, (ℤ/109242)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C32×C17 |
| socle, prime radical | C23×C32×C17 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
980 conjugacy classes of subgroups.
29376 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.