Finite Group DatabasebetaFinite Group Databasebeta| order | 10352 |
| automorphism | Aut(G) order 13374784 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2588 |
| Sylow | C647 ⋊ Q16 |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,647|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^646,c^b=cd,e^b=e^6462591 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35208356, #35208357, #35208358, … |
| maximal normal subgroup of | #35208356, #35208357, #35208358, … |
| maximal quotient of | #35208337, #35208346, C2×Dic2588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10352, 31);