Finite Group DatabasebetaFinite Group Databasebeta| order | 16896 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3523215360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4 |
| abelian | C23×C3×C4×C11×C16 |
| multiplicative | (ℤ/40664)ˣ, (ℤ/41055)ˣ, (ℤ/43792)ˣ, (ℤ/45560)ˣ, (ℤ/51520)ˣ, (ℤ/54672)ˣ, (ℤ/54740)ˣ, (ℤ/56304)ˣ, (ℤ/57408)ˣ, (ℤ/60996)ˣ, (ℤ/64320)ˣ, (ℤ/66240)ˣ, (ℤ/68340)ˣ, (ℤ/70380)ˣ, (ℤ/82110)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C25×C3×C11 |
| socle, prime radical | C25×C3×C11 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12552 conjugacy classes of subgroups.
16896 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.