Finite Group DatabasebetaFinite Group Databasebeta| order | 31392 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 165888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C32×C16×C109 |
| multiplicative | (ℤ/36631)ˣ, (ℤ/47097)ˣ, (ℤ/73262)ˣ, (ℤ/94194)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C22×C32×C109 |
| socle, prime radical | C22×C32×C109 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
168 conjugacy classes of subgroups.
31392 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.