Finite Group DatabasebetaFinite Group Databasebeta| order | 19152 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 82944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C7×C8×C19 |
| multiplicative | (ℤ/19651)ˣ, (ℤ/22393)ˣ, (ℤ/39302)ˣ, (ℤ/44786)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C22×C32×C7×C19 |
| socle, prime radical | C22×C32×C7×C19 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
264 conjugacy classes of subgroups.
19152 conjugacy classes. The character table is too large to display.
| automorphism group of | C43×C457 |
| outer automorphism group of | C43×C457 |
Past the SmallGroups library coverage — no SmallGroups id.