Finite Group DatabasebetaFinite Group Databasebeta| order | 31104 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 123834728448 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C32×C4×C9 |
| abelian | C22×C3×C4×C8×C92 |
| multiplicative | (ℤ/48545)ˣ, (ℤ/54093)ˣ, (ℤ/56721)ˣ, (ℤ/62415)ˣ, (ℤ/68985)ˣ, (ℤ/72124)ˣ, (ℤ/75628)ˣ, (ℤ/97090)ˣ, (ℤ/97236)ˣ, (ℤ/102492)ˣ, (ℤ/108186)ˣ, (ℤ/113442)ˣ, (ℤ/124830)ˣ, (ℤ/137970)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32×C4 | C24×C33 |
| socle, prime radical | C24×C33 | C2×C32×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
47880 conjugacy classes of subgroups.
31104 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.