Finite Group DatabasebetaFinite Group Databasebeta| order | 24288 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4399718400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C25×C3×C11×C23 |
| multiplicative | (ℤ/60536)ˣ, (ℤ/75576)ˣ, (ℤ/76728)ˣ, (ℤ/77832)ˣ, (ℤ/88872)ˣ, (ℤ/90804)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2992 conjugacy classes of subgroups.
24288 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.