Finite Group DatabasebetaFinite Group Databasebeta| order | 28560 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 15482880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C3×C5×C7×C17 |
| multiplicative | (ℤ/55209)ˣ, (ℤ/58504)ˣ, (ℤ/59272)ˣ, (ℤ/73612)ˣ, (ℤ/85704)ˣ, (ℤ/87756)ˣ, (ℤ/88908)ˣ, (ℤ/94644)ˣ, (ℤ/110418)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1072 conjugacy classes of subgroups.
28560 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.