Finite Group DatabasebetaFinite Group Databasebeta| order | 22120 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14976 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C5×C7×C79 |
| multiplicative | (ℤ/22507)ˣ, (ℤ/24343)ˣ, (ℤ/27655)ˣ, (ℤ/45014)ˣ, (ℤ/48686)ˣ, (ℤ/55310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C5×C7×C79 |
| socle, prime radical | C22×C5×C7×C79 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
22120 conjugacy classes. The character table is too large to display.
| automorphism group of | C71×C317 |
| outer automorphism group of | C71×C317 |
Past the SmallGroups library coverage — no SmallGroups id.