Finite Group DatabasebetaFinite Group Databasebeta| order | 31750 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C4×C7×C9×C25 (order 12600) · Inn(G) = C1 · Out(G) = C2×C4×C7×C9×C25 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C31750 |
| abelian | C2×C125×C127 |
| multiplicative | (ℤ/31751)ˣ, (ℤ/63502)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C25 | C2×C5×C127 |
| socle, prime radical | C2×C5×C127 | C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
31750 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15875, C2×D15875 |
| maximal subgroup of | Dic15875, C2×D15875 |
| maximal normal subgroup of | Dic15875, C2×D15875 |
| automorphism group of | C31751 |
| outer automorphism group of | C31751 |
Past the SmallGroups library coverage — no SmallGroups id.