Finite Group DatabasebetaFinite Group Databasebeta| order | 4496 |
| automorphism | Aut(G) order 2517760 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1124 |
| Sylow | C281 ⋊ Q16 |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^4,281|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^280,c^b=cd,e^b=e^2801127 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3372, Dic5620, Dic7868, … |
| maximal quotient of | Dic3372, Dic5620, Dic7868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4496, 31);