Finite Group DatabasebetaFinite Group Databasebeta| order | 21648 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 153600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C11×C41 |
| multiplicative | (ℤ/24817)ˣ, (ℤ/27805)ˣ, (ℤ/40605)ˣ, (ℤ/43304)ˣ, (ℤ/43312)ˣ, (ℤ/49634)ˣ, (ℤ/54140)ˣ, (ℤ/55610)ˣ, (ℤ/64956)ˣ, (ℤ/81210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C11×C41 |
| socle, prime radical | C23×C3×C11×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
21648 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C23×C83 |
| outer automorphism group of | C13×C23×C83 |
Past the SmallGroups library coverage — no SmallGroups id.