Finite Group DatabasebetaFinite Group Databasebeta| order | 27600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 84480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C3×C42×C23×C25 |
| multiplicative | (ℤ/27977)ˣ, (ℤ/34625)ˣ, (ℤ/55954)ˣ, (ℤ/69250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C5 | C22×C3×C5×C23 |
| socle, prime radical | C22×C3×C5×C23 | C22×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
180 conjugacy classes of subgroups.
27600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.