Finite Group DatabasebetaFinite Group Databasebeta| order | 17184 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7655424 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C179 |
| multiplicative | (ℤ/37336)ˣ, (ℤ/37695)ˣ, (ℤ/40208)ˣ, (ℤ/50260)ˣ, (ℤ/51696)ˣ, (ℤ/56004)ˣ, (ℤ/64620)ˣ, (ℤ/75390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C179 |
| socle, prime radical | C24×C3×C179 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
472 conjugacy classes of subgroups.
17184 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.