Finite Group DatabasebetaFinite Group Databasebeta| order | 18816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 16515072 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C7 |
| abelian | C2×C3×C4×C72×C16 |
| multiplicative | (ℤ/21199)ˣ, (ℤ/22939)ˣ, (ℤ/24157)ˣ, (ℤ/24295)ˣ, (ℤ/27685)ˣ, (ℤ/29319)ˣ, (ℤ/29493)ˣ, (ℤ/39092)ˣ, (ℤ/42398)ˣ, (ℤ/45878)ˣ, (ℤ/48314)ˣ, (ℤ/48590)ˣ, (ℤ/55370)ˣ, (ℤ/58638)ˣ, (ℤ/58986)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C3×C72 |
| socle, prime radical | C23×C3×C72 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2160 conjugacy classes of subgroups.
18816 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C29×C43 |
| outer automorphism group of | C17×C29×C43 |
Past the SmallGroups library coverage — no SmallGroups id.