Finite Group DatabasebetaFinite Group Databasebeta| order | 23904 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6045696 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C42×C83 |
| multiplicative | (ℤ/32435)ˣ, (ℤ/34895)ˣ, (ℤ/38883)ˣ, (ℤ/44865)ˣ, (ℤ/51844)ˣ, (ℤ/64870)ˣ, (ℤ/69790)ˣ, (ℤ/77766)ˣ, (ℤ/89730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C32×C83 |
| socle, prime radical | C23×C32×C83 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
23904 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.