Finite Group DatabasebetaFinite Group Databasebeta| order | 17280 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14155776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C5×C8×C27 |
| multiplicative | (ℤ/35752)ˣ, (ℤ/38368)ˣ, (ℤ/43360)ˣ, (ℤ/51936)ˣ, (ℤ/53136)ˣ, (ℤ/53628)ˣ, (ℤ/64800)ˣ, (ℤ/66420)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C9 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C2×C4×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3040 conjugacy classes of subgroups.
17280 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.