Finite Group DatabasebetaFinite Group Databasebeta| order | 22032 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C17×C27 |
| multiplicative | (ℤ/32165)ˣ, (ℤ/33681)ˣ, (ℤ/35841)ˣ, (ℤ/41355)ˣ, (ℤ/41715)ˣ, (ℤ/44908)ˣ, (ℤ/47788)ˣ, (ℤ/64330)ˣ, (ℤ/67362)ˣ, (ℤ/71682)ˣ, (ℤ/82710)ˣ, (ℤ/83430)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C23×C32×C17 |
| socle, prime radical | C23×C32×C17 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
756 conjugacy classes of subgroups.
22032 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.