Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C13×#107 ⋊ C4 |
| Sylow | C13 ⋊ #1776 |
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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=e,b^2=f,c^2=de,d^2=g,e^2=g,b^a=bd,c^a=cg,h^a=h^5,d^b=dg,e^b=eg,h^c=h^8,h^e=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | #16789543, #16789544, #16789545, … |
| maximal normal subgroup of | #16789543, #16789544, #16789545, … |
| maximal quotient of | #16780923, #16780927, #16780935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20325);