Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C499 ⋊ C2 |
| Sylow | C499 ⋊ D16 |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^4981754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D16×D499, C2×#30630292, #44543528, … |
| maximal normal subgroup of | D16×D499, C2×#30630292, #44543528, … |
| maximal quotient of | #44542898, #44542899, #44542923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 87);