Finite Group DatabasebetaFinite Group Databasebeta| order | 22848 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28311552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C42×C7×C17 |
| multiplicative | (ℤ/44805)ˣ, (ℤ/46605)ˣ, (ℤ/47792)ˣ, (ℤ/49712)ˣ, (ℤ/57160)ˣ, (ℤ/59740)ˣ, (ℤ/62140)ˣ, (ℤ/68592)ˣ, (ℤ/85740)ˣ, (ℤ/89610)ˣ, (ℤ/93210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C3×C7×C17 |
| socle, prime radical | C24×C3×C7×C17 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1992 conjugacy classes of subgroups.
22848 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.