Finite Group DatabasebetaFinite Group Databasebeta| order | 23184 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 152064 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C7×C9×C23 |
| multiplicative | (ℤ/25897)ˣ, (ℤ/29845)ˣ, (ℤ/36801)ˣ, (ℤ/51794)ˣ, (ℤ/59690)ˣ, (ℤ/73602)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C3×C7×C23 |
| socle, prime radical | C23×C3×C7×C23 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
23184 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C29×C47 |
| outer automorphism group of | C19×C29×C47 |
Past the SmallGroups library coverage — no SmallGroups id.