Finite Group DatabasebetaFinite Group Databasebeta| order | 31600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C42×C5×C13 (order 12480) · Inn(G) = C1 · Out(G) = C22×C3×C42×C5×C13 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C31600 |
| abelian | C16×C25×C79 |
| multiplicative | (ℤ/31601)ˣ, (ℤ/63202)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C8 | C2×C5×C79 |
| socle, prime radical | C2×C5×C79 | C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30 conjugacy classes of subgroups.
31600 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15800, D31600 |
| maximal subgroup of | Dic15800, D31600 |
| maximal normal subgroup of | Dic15800, D31600 |
| automorphism group of | C31601 |
| outer automorphism group of | C31601 |
Past the SmallGroups library coverage — no SmallGroups id.