Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 37158912 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C42×C9×C49 |
| multiplicative | (ℤ/56145)ˣ, (ℤ/58312)ˣ, (ℤ/59888)ˣ, (ℤ/70640)ˣ, (ℤ/74860)ˣ, (ℤ/85104)ˣ, (ℤ/87468)ˣ, (ℤ/106380)ˣ, (ℤ/112290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C7 | C24×C3×C7 |
| socle, prime radical | C24×C3×C7 | C22×C3×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2241 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.