Finite Group DatabasebetaFinite Group Databasebeta| order | 18592 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 15744 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C7×C16×C83 |
| multiplicative | (ℤ/18871)ˣ, (ℤ/19771)ˣ, (ℤ/37742)ˣ, (ℤ/39542)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C7×C83 |
| socle, prime radical | C22×C7×C83 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
56 conjugacy classes of subgroups.
18592 conjugacy classes. The character table is too large to display.
| automorphism group of | C113×C167, C17×C1163 |
| outer automorphism group of | C113×C167, C17×C1163 |
Past the SmallGroups library coverage — no SmallGroups id.