Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1394 |
172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=e,c^2=g,d^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^8,d^b=dfg,h^b=h^12,d^c=dg,h^d=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16777864, #16777865, #16777920, … |
| maximal normal subgroup of | #16777864, #16777865, #16777920, … |
| maximal quotient of | #16777252, #16777308, #16777346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19608);