Finite Group DatabasebetaFinite Group Databasebeta| order | 27648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 679477248 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C16 |
| abelian | C22×C162×C27 |
| multiplicative | (ℤ/58888)ˣ, (ℤ/83136)ˣ, (ℤ/88128)ˣ, (ℤ/88332)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C82×C9 | C24×C3 |
| socle, prime radical | C24×C3 | C82×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6292 conjugacy classes of subgroups.
27648 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.