Finite Group DatabasebetaFinite Group Databasebeta| order | 22176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 92160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C7×C11×C16 |
| multiplicative | (ℤ/22579)ˣ, (ℤ/25879)ˣ, (ℤ/33273)ˣ, (ℤ/45158)ˣ, (ℤ/51758)ˣ, (ℤ/66546)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C32×C7×C11 |
| socle, prime radical | C22×C32×C7×C11 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
336 conjugacy classes of subgroups.
22176 conjugacy classes. The character table is too large to display.
| automorphism group of | C67×C337 |
| outer automorphism group of | C67×C337 |
Past the SmallGroups library coverage — no SmallGroups id.