Finite Group DatabasebetaFinite Group Databasebeta| order | 17928 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1487808 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C9×C83 |
| multiplicative | (ℤ/22211)ˣ, (ℤ/28443)ˣ, (ℤ/28557)ˣ, (ℤ/31563)ˣ, (ℤ/37924)ˣ, (ℤ/44422)ˣ, (ℤ/53892)ˣ, (ℤ/56886)ˣ, (ℤ/57114)ˣ, (ℤ/63126)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C83 |
| socle, prime radical | C23×C32×C83 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
17928 conjugacy classes. The character table is too large to display.
| automorphism group of | C7×C19×C167, C7×C27×C167 |
| outer automorphism group of | C7×C19×C167, C7×C27×C167 |
Past the SmallGroups library coverage — no SmallGroups id.