Finite Group DatabasebetaFinite Group Databasebeta| order | 31392 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C4×C8×C27 (order 10368) · Inn(G) = C1 · Out(G) = C22×C3×C4×C8×C27 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C31392 |
| abelian | C9×C32×C109 |
| multiplicative | (ℤ/31393)ˣ, (ℤ/62786)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C16 | C2×C3×C109 |
| socle, prime radical | C2×C3×C109 | C3×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36 conjugacy classes of subgroups.
31392 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15696, D31392 |
| maximal subgroup of | Dic15696, D31392 |
| maximal normal subgroup of | Dic15696, D31392 |
| automorphism group of | C31393 |
| outer automorphism group of | C31393 |
Past the SmallGroups library coverage — no SmallGroups id.