Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C13×#376 ⋊ C2 |
| Sylow | C13 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 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,b^2=g,c^2=f,d^2=e,b^a=be,h^c=h^12320 conjugacy classes — view the full character table.
| maximal subgroup of | #15752316, #15752322, #15753113, … |
| maximal normal subgroup of | #15752316, #15752322, #15753113, … |
| maximal quotient of | Dic13×#376, C4×#11718327, C4×#11718310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6849);