Finite Group DatabasebetaFinite Group Databasebeta| order | 31232 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C4×C5×C128 (order 15360) · Inn(G) = C1 · Out(G) = C2×C3×C4×C5×C128 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C31232 |
| abelian | C61×C512 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C256 | C2×C61 |
| socle, prime radical | C2×C61 | C256 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
31232 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15616, D31232 |
| maximal subgroup of | Dic15616, D31232 |
| maximal normal subgroup of | Dic15616, D31232 |
Past the SmallGroups library coverage — no SmallGroups id.