Finite Group DatabasebetaFinite Group Databasebeta| order | 29064 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 346752 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C7×C173 |
| multiplicative | (ℤ/44763)ˣ, (ℤ/50883)ˣ, (ℤ/51009)ˣ, (ℤ/59684)ˣ, (ℤ/67844)ˣ, (ℤ/68012)ˣ, (ℤ/87228)ˣ, (ℤ/89526)ˣ, (ℤ/101766)ˣ, (ℤ/102018)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
29064 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.