Finite Group DatabasebetaFinite Group Databasebeta| order | 23232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1135411200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C11 |
| abelian | C23×C3×C8×C112 |
| multiplicative | (ℤ/42987)ˣ, (ℤ/47704)ˣ, (ℤ/49312)ˣ, (ℤ/57316)ˣ, (ℤ/71556)ˣ, (ℤ/73692)ˣ, (ℤ/85974)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C3×C112 |
| socle, prime radical | C24×C3×C112 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4732 conjugacy classes of subgroups.
23232 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.