Finite Group DatabasebetaFinite Group Databasebeta| order | 29232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1548288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C7×C29 |
| multiplicative | (ℤ/32981)ˣ, (ℤ/37583)ˣ, (ℤ/45021)ˣ, (ℤ/51177)ˣ, (ℤ/51303)ˣ, (ℤ/52983)ˣ, (ℤ/60028)ˣ, (ℤ/65962)ˣ, (ℤ/68236)ˣ, (ℤ/68404)ˣ, (ℤ/75166)ˣ, (ℤ/87732)ˣ, (ℤ/90042)ˣ, (ℤ/102354)ˣ, (ℤ/102606)ˣ, (ℤ/105966)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C7×C29 |
| socle, prime radical | C23×C32×C7×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
29232 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.