Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 998831554560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3×C7 |
| abelian | C24×C32×C4×C72 |
| multiplicative | (ℤ/69832)ˣ, (ℤ/84280)ˣ, (ℤ/89784)ˣ, (ℤ/101136)ˣ, (ℤ/102312)ˣ, (ℤ/104748)ˣ, (ℤ/126420)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C32×C72 |
| socle, prime radical | C25×C32×C72 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40860 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.