Finite Group DatabasebetaFinite Group Databasebeta| order | 27280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 230400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C5×C11×C31 |
| multiplicative | (ℤ/35765)ˣ, (ℤ/37565)ˣ, (ℤ/51225)ˣ, (ℤ/68300)ˣ, (ℤ/71530)ˣ, (ℤ/75130)ˣ, (ℤ/102450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C5×C11×C31 |
| socle, prime radical | C23×C5×C11×C31 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
27280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.