Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8918138880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C24×C3×C5×C8×C9 |
| multiplicative | (ℤ/43624)ˣ, (ℤ/44968)ˣ, (ℤ/46816)ˣ, (ℤ/54312)ˣ, (ℤ/56088)ˣ, (ℤ/56544)ˣ, (ℤ/57816)ˣ, (ℤ/60192)ˣ, (ℤ/61992)ˣ, (ℤ/65436)ˣ, (ℤ/66528)ˣ, (ℤ/67452)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C25×C32×C5 |
| socle, prime radical | C25×C32×C5 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
19760 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.