Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C31 ⋊ C2 |
| Sylow | C31 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|b^2=e,c^2=d,c^a=ce,f^a=f^30260 conjugacy classes — view the full character table.
| maximal subgroup of | #14521003, #14521006, #14521064, … |
| maximal normal subgroup of | #14521003, #14521006, #14521064, … |
| maximal quotient of | #14520895, C4×(C2×D31)⋊C4, C4×Dic31⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 67);