Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D499)⋊C8 |
| Fitting | C2×C8×C499 ⋊ C2 |
| Sylow | C499 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=d,d^2=e,b^a=bc,f^b=f^4984004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D499, C2×(C2×D499)⋊C8, #44543060, … |
| maximal normal subgroup of | C22⋊C8×D499, C2×(C2×D499)⋊C8, #44543060, … |
| maximal quotient of | #44542821, #44542823, #44542825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 58);