Finite Group DatabasebetaFinite Group Databasebeta| order | 31536 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C4×C8×C92 (order 10368) · Inn(G) = C1 · Out(G) = C22×C4×C8×C92 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C31536 |
| abelian | C16×C27×C73 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C9 | C2×C3×C73 |
| socle, prime radical | C2×C3×C73 | C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
31536 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15768, D31536 |
| maximal subgroup of | Dic15768, D31536 |
| maximal normal subgroup of | Dic15768, D31536 |
Past the SmallGroups library coverage — no SmallGroups id.