Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2381 |
424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^12,c^b=cef,d^b=de206 conjugacy classes — view the full character table.
| maximal subgroup of | #15760459, #15760462, #15760464, … |
| maximal normal subgroup of | #15760459, #15760462, #15760464, … |
| maximal quotient of | #15784546, #15784569, #15784573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7691);