Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic31⋊C8 |
| Sylow | C31 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^5,31|a^2=d,b^2=c,c^2=e,b^a=bd,f^a=f^30260 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C8×D31, C2×Dic31⋊C8, #14521071, … |
| maximal normal subgroup of | C4⋊C8×D31, C2×Dic31⋊C8, #14521071, … |
| maximal quotient of | #14520799, #14520801, #14520803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 20);