Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D491 |
| Fitting | C2×Q8×C491 ⋊ C2 |
| Sylow | C491 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
2470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D491, #103×D491, #44536732, … |
| maximal normal subgroup of | #101×D491, #103×D491, #44536732, … |
| maximal quotient of | C2×C4⋊C4×D491, C4×Q8×D491, C2×#30628302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 185);