Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C13×#379 ⋊ C2 |
| Sylow | C13 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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=g,d^2=g,b^a=be,c^a=cf,h^d=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15772166, #15772364, #15868904, … |
| maximal normal subgroup of | #15772166, #15772364, #15868904, … |
| maximal quotient of | #15784063, #15784083, Dic13×#379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7009);