Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C499 ⋊ C2 |
| Sylow | C499 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^498,c^b=cd,d^b=de,f^b=f^4983995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D499, C2×#30630296, #44543529, … |
| maximal normal subgroup of | SD32×D499, C2×#30630296, #44543529, … |
| maximal quotient of | #44542900, #44542903, #44542926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 91);