Finite Group DatabasebetaFinite Group Databasebeta| order | 21216 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C13×C17 |
| multiplicative | (ℤ/43672)ˣ, (ℤ/46072)ˣ, (ℤ/46515)ˣ, (ℤ/49616)ˣ, (ℤ/53080)ˣ, (ℤ/62020)ˣ, (ℤ/63696)ˣ, (ℤ/63792)ˣ, (ℤ/65508)ˣ, (ℤ/69108)ˣ, (ℤ/79620)ˣ, (ℤ/79740)ˣ, (ℤ/93030)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C13×C17 |
| socle, prime radical | C24×C3×C13×C17 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
21216 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.