Finite Group DatabasebetaFinite Group Databasebeta| order | 31104 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4623163195392 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C33×C4 |
| abelian | C23×C32×C42×C27 |
| multiplicative | (ℤ/79352)ˣ, (ℤ/102024)ˣ, (ℤ/109872)ˣ, (ℤ/117936)ˣ, (ℤ/119028)ˣ, (ℤ/137340)ˣ, (ℤ/147420)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C9 | C25×C33 |
| socle, prime radical | C25×C33 | C22×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108000 conjugacy classes of subgroups.
31104 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.