Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C499 ⋊ M32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^4984004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44542875, #44542876, #44542879, … |
| maximal normal subgroup of | #44542875, #44542876, #44542879, … |
| maximal quotient of | #44542874, C22⋊(C499⋊C16), C4⋊(C499⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 86);