Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14269022208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4×C7 |
| abelian | C22×C32×C42×C72 |
| multiplicative | (ℤ/43645)ˣ, (ℤ/48633)ˣ, (ℤ/55419)ˣ, (ℤ/56115)ˣ, (ℤ/63945)ˣ, (ℤ/64844)ˣ, (ℤ/73892)ˣ, (ℤ/87290)ˣ, (ℤ/97266)ˣ, (ℤ/110838)ˣ, (ℤ/112230)ˣ, (ℤ/127890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C32×C72 |
| socle, prime radical | C24×C32×C72 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
14940 conjugacy classes of subgroups.
28224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.