Finite Group DatabasebetaFinite Group Databasebeta| order | 30400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 17694720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C4×C52×C8×C19 |
| multiplicative | (ℤ/39155)ˣ, (ℤ/41855)ˣ, (ℤ/57075)ˣ, (ℤ/76100)ˣ, (ℤ/78310)ˣ, (ℤ/83710)ˣ, (ℤ/114150)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C52×C19 |
| socle, prime radical | C23×C52×C19 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
30400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.