Finite Group DatabasebetaFinite Group Databasebeta| order | 14816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic463⋊C8 |
| Sylow | C463 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14816 |
Polycyclic presentation:
2^5,463|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^4623716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C8×D463, C2×Dic463⋊C8, #44444815, … |
| maximal normal subgroup of | C4⋊C8×D463, C2×Dic463⋊C8, #44444815, … |
| maximal quotient of | #44444543, #44444545, #44444547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14816, 75);