Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 184025088 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C33×C4 |
| abelian | C2×C33×C4×C5×C16 |
| multiplicative | (ℤ/21931)ˣ, (ℤ/28197)ˣ, (ℤ/43862)ˣ, (ℤ/56394)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C33×C5 |
| socle, prime radical | C23×C33×C5 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6048 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C13×C241 |
| outer automorphism group of | C7×C13×C241 |
Past the SmallGroups library coverage — no SmallGroups id.