Finite Group DatabasebetaFinite Group Databasebeta| order | 15968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C499 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7984 |
Polycyclic presentation:
2^5,499|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^4982504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D499, C2×#30630328, #44543604, … |
| maximal normal subgroup of | C22⋊Q8×D499, C2×#30630328, #44543604, … |
| maximal quotient of | #44542956, #44542970, #44542973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15968, 123);