Finite Group DatabasebetaFinite Group Databasebeta| order | 31968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5971968 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C42×C9×C37 |
| multiplicative | (ℤ/36803)ˣ, (ℤ/38591)ˣ, (ℤ/41255)ˣ, (ℤ/47915)ˣ, (ℤ/49617)ˣ, (ℤ/52299)ˣ, (ℤ/53391)ˣ, (ℤ/61605)ˣ, (ℤ/71188)ˣ, (ℤ/73606)ˣ, (ℤ/77182)ˣ, (ℤ/82510)ˣ, (ℤ/95830)ˣ, (ℤ/99234)ˣ, (ℤ/104598)ˣ, (ℤ/106782)ˣ, (ℤ/123210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C32×C37 |
| socle, prime radical | C23×C32×C37 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
31968 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.