Finite Group DatabasebetaFinite Group Databasebeta| order | 18480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C5×C7×C8×C11 |
| multiplicative | (ℤ/18779)ˣ, (ℤ/18827)ˣ, (ℤ/18983)ˣ, (ℤ/19127)ˣ, (ℤ/27723)ˣ, (ℤ/36964)ˣ, (ℤ/37558)ˣ, (ℤ/37654)ˣ, (ℤ/37966)ˣ, (ℤ/38254)ˣ, (ℤ/55446)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C3×C5×C7×C11 |
| socle, prime radical | C22×C3×C5×C7×C11 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
176 conjugacy classes of subgroups.
18480 conjugacy classes. The character table is too large to display.
| automorphism group of | C89×C211, C67×C281, C41×C463, … |
| outer automorphism group of | C89×C211, C67×C281, C41×C463, … |
Past the SmallGroups library coverage — no SmallGroups id.