Finite Group DatabasebetaFinite Group Databasebeta| order | 22040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 338688 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C5×C19×C29 |
| multiplicative | (ℤ/33807)ˣ, (ℤ/36399)ˣ, (ℤ/45076)ˣ, (ℤ/48532)ˣ, (ℤ/67614)ˣ, (ℤ/72798)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
22040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.