Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2991 |
394 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^8,c^b=ceg,h^b=h^12,h^d=h^12,h^f=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783825, #16783829, #16783833, … |
| maximal normal subgroup of | #16783825, #16783829, #16783833, … |
| maximal quotient of | #16797610, #16797611, #16797694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21443);