Finite Group DatabasebetaFinite Group Databasebeta| order | 18216 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1774080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C11×C23 |
| multiplicative | (ℤ/22043)ˣ, (ℤ/22379)ˣ, (ℤ/27939)ˣ, (ℤ/28341)ˣ, (ℤ/28773)ˣ, (ℤ/33327)ˣ, (ℤ/37252)ˣ, (ℤ/44086)ˣ, (ℤ/44758)ˣ, (ℤ/55878)ˣ, (ℤ/56682)ˣ, (ℤ/57546)ˣ, (ℤ/66654)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
384 conjugacy classes of subgroups.
18216 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C47×C67 |
| outer automorphism group of | C7×C47×C67 |
Past the SmallGroups library coverage — no SmallGroups id.