Finite Group DatabasebetaFinite Group Databasebeta| order | 30400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 371589120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C5 |
| abelian | C23×C52×C8×C19 |
| multiplicative | (ℤ/62648)ˣ, (ℤ/66968)ˣ, (ℤ/67232)ˣ, (ℤ/93972)ˣ, (ℤ/100452)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C52×C19 |
| socle, prime radical | C24×C52×C19 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2704 conjugacy classes of subgroups.
30400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.