Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D31 |
| Fitting | C2×Q8×C31 ⋊ C2 |
| Sylow | C31 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #101×D31, #103×D31, #14521056, … |
| maximal normal subgroup of | #101×D31, #103×D31, #14521056, … |
| maximal quotient of | C2×C4⋊C4×D31, C4×Q8×D31, C2×#11758464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 180);