Finite Group DatabasebetaFinite Group Databasebeta| order | 27200 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 655360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C8×C17×C25 |
| multiplicative | (ℤ/41511)ˣ, (ℤ/51375)ˣ, (ℤ/55348)ˣ, (ℤ/68500)ˣ, (ℤ/83022)ˣ, (ℤ/102750)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C23×C5×C17 |
| socle, prime radical | C23×C5×C17 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
486 conjugacy classes of subgroups.
27200 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.