Finite Group DatabasebetaFinite Group Databasebeta| order | 22104 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14688 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C9×C307 |
| multiplicative | (ℤ/23351)ˣ, (ℤ/27635)ˣ, (ℤ/33183)ˣ, (ℤ/46702)ˣ, (ℤ/55270)ˣ, (ℤ/66366)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C3×C307 |
| socle, prime radical | C22×C3×C307 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
48 conjugacy classes of subgroups.
22104 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C1229 |
| outer automorphism group of | C19×C1229 |
Past the SmallGroups library coverage — no SmallGroups id.