Finite Group DatabasebetaFinite Group Databasebeta| order | 30360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C5×C11×C23 |
| multiplicative | (ℤ/30887)ˣ, (ℤ/31067)ˣ, (ℤ/31403)ˣ, (ℤ/31763)ˣ, (ℤ/32269)ˣ, (ℤ/32903)ˣ, (ℤ/33407)ˣ, (ℤ/33517)ˣ, (ℤ/37955)ˣ, (ℤ/61774)ˣ, (ℤ/62134)ˣ, (ℤ/62806)ˣ, (ℤ/63526)ˣ, (ℤ/64538)ˣ, (ℤ/65806)ˣ, (ℤ/66814)ˣ, (ℤ/67034)ˣ, (ℤ/75910)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C5×C11×C23 |
| socle, prime radical | C22×C3×C5×C11×C23 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
30360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.