Finite Group DatabasebetaFinite Group Databasebeta| order | 27224 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 551040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C41×C83 |
| multiplicative | (ℤ/41583)ˣ, (ℤ/55112)ˣ, (ℤ/55444)ˣ, (ℤ/82668)ˣ, (ℤ/83166)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
27224 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.