Finite Group DatabasebetaFinite Group Databasebeta| order | 28560 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C5×C7×C8×C17 |
| multiplicative | (ℤ/28907)ˣ, (ℤ/28943)ˣ, (ℤ/29039)ˣ, (ℤ/29543)ˣ, (ℤ/31427)ˣ, (ℤ/42843)ˣ, (ℤ/57124)ˣ, (ℤ/57814)ˣ, (ℤ/57886)ˣ, (ℤ/58078)ˣ, (ℤ/59086)ˣ, (ℤ/62854)ˣ, (ℤ/85686)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C3×C5×C7×C17 |
| socle, prime radical | C22×C3×C5×C7×C17 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
176 conjugacy classes of subgroups.
28560 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.