Finite Group DatabasebetaFinite Group Databasebeta| order | 22176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 138240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C7×C8×C9×C11 |
| multiplicative | (ℤ/33909)ˣ, (ℤ/35169)ˣ, (ℤ/45212)ˣ, (ℤ/46892)ˣ, (ℤ/66636)ˣ, (ℤ/67818)ˣ, (ℤ/70338)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C23×C3×C7×C11 |
| socle, prime radical | C23×C3×C7×C11 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
456 conjugacy classes of subgroups.
22176 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.