Finite Group DatabasebetaFinite Group Databasebeta| order | 27440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 112896 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C42×C5×C343 |
| multiplicative | (ℤ/34325)ˣ, (ℤ/68650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C49 | C22×C5×C7 |
| socle, prime radical | C22×C5×C7 | C22×C49 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
27440 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.