Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 839808 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C9 |
| abelian | C2×C9×C16×C81 |
| multiplicative | (ℤ/24643)ˣ, (ℤ/35019)ˣ, (ℤ/49286)ˣ, (ℤ/70038)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8×C27 | C22×C32 |
| socle, prime radical | C22×C32 | C3×C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
686 conjugacy classes of subgroups.
23328 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1297 |
| outer automorphism group of | C19×C1297 |
Past the SmallGroups library coverage — no SmallGroups id.