Finite Group DatabasebetaFinite Group Databasebeta| order | 30456 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 119232 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C27×C47 |
| multiplicative | (ℤ/30847)ˣ, (ℤ/33007)ˣ, (ℤ/35539)ˣ, (ℤ/45693)ˣ, (ℤ/61694)ˣ, (ℤ/66014)ˣ, (ℤ/71078)ˣ, (ℤ/91386)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C22×C32×C47 |
| socle, prime radical | C22×C32×C47 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
224 conjugacy classes of subgroups.
30456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.