Finite Group DatabasebetaFinite Group Databasebeta| order | 22400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 660602880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C43×C7×C25 |
| multiplicative | (ℤ/43935)ˣ, (ℤ/46864)ˣ, (ℤ/56080)ˣ, (ℤ/58000)ˣ, (ℤ/58580)ˣ, (ℤ/87870)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C5 | C24×C5×C7 |
| socle, prime radical | C24×C5×C7 | C23×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3816 conjugacy classes of subgroups.
22400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.