Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 516096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C8×C9×C49 |
| multiplicative | (ℤ/43143)ˣ, (ℤ/52935)ˣ, (ℤ/56464)ˣ, (ℤ/57524)ˣ, (ℤ/70580)ˣ, (ℤ/86286)ˣ, (ℤ/105870)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4×C7 | C23×C3×C7 |
| socle, prime radical | C23×C3×C7 | C2×C3×C4×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
729 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.