Finite Group DatabasebetaFinite Group Databasebeta| order | 21384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 272160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C11×C243 |
| multiplicative | (ℤ/33603)ˣ, (ℤ/42776)ˣ, (ℤ/44804)ˣ, (ℤ/64164)ˣ, (ℤ/67068)ˣ, (ℤ/67206)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C81 | C23×C3×C11 |
| socle, prime radical | C23×C3×C11 | C81 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
21384 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.