Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1769472 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C4×C5×C9×C16 |
| multiplicative | (ℤ/19499)ˣ, (ℤ/19703)ˣ, (ℤ/21539)ˣ, (ℤ/22895)ˣ, (ℤ/26751)ˣ, (ℤ/27693)ˣ, (ℤ/27999)ˣ, (ℤ/32535)ˣ, (ℤ/35668)ˣ, (ℤ/38998)ˣ, (ℤ/39406)ˣ, (ℤ/43078)ˣ, (ℤ/45790)ˣ, (ℤ/53502)ˣ, (ℤ/55386)ˣ, (ℤ/55998)ˣ, (ℤ/65070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C8 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2160 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C31×C37, C17×C19×C61, C7×C17×C181, … |
| outer automorphism group of | C17×C31×C37, C17×C19×C61, C7×C17×C181, … |
Past the SmallGroups library coverage — no SmallGroups id.