Finite Group DatabasebetaFinite Group Databasebeta| order | 22368 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 712704 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C233 |
| multiplicative | (ℤ/30355)ˣ, (ℤ/41955)ˣ, (ℤ/44752)ˣ, (ℤ/55940)ˣ, (ℤ/60710)ˣ, (ℤ/83910)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C233 |
| socle, prime radical | C23×C3×C233 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
22368 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.