Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C499 ⋊ C2 |
| Sylow | C499 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=e,c^2=d,b^a=bd,f^b=f^498,f^c=f^4982510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44543091, #44543093, #44543101, … |
| maximal normal subgroup of | #44543091, #44543093, #44543101, … |
| maximal quotient of | #44542943, #44542945, C4⋊C4×Dic499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 104);