Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 42467328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43 |
| abelian | C3×C42×C5×C8×C9 |
| multiplicative | (ℤ/19721)ˣ, (ℤ/22265)ˣ, (ℤ/23725)ˣ, (ℤ/39442)ˣ, (ℤ/44530)ˣ, (ℤ/47450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C4 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C22×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4080 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C37×C41 |
| outer automorphism group of | C13×C37×C41 |
Past the SmallGroups library coverage — no SmallGroups id.