Finite Group DatabasebetaFinite Group Databasebeta| order | 27680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 264192 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C8×C173 |
| multiplicative | (ℤ/42681)ˣ, (ℤ/56908)ˣ, (ℤ/85362)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C23×C5×C173 |
| socle, prime radical | C23×C5×C173 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
152 conjugacy classes of subgroups.
27680 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.