Finite Group DatabasebetaFinite Group Databasebeta| order | 30400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 53084160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C19×C25 |
| multiplicative | (ℤ/76040)ˣ, (ℤ/91248)ˣ, (ℤ/114060)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C5 | C24×C5×C19 |
| socle, prime radical | C24×C5×C19 | C22×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1494 conjugacy classes of subgroups.
30400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.