Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C499 ⋊ C2 |
| Sylow | C499 ⋊ #100 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3992 |
Polycyclic presentation:
2^5,499|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^4982501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D499, C2×#30630267, #44543080, … |
| maximal normal subgroup of | #100×D499, C2×#30630267, #44543080, … |
| maximal quotient of | #44542821, #44542837, #44542841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 62);