Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2320 |
444 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15759848, #15759852, #15759862, … |
| maximal normal subgroup of | #15759848, #15759852, #15759862, … |
| maximal quotient of | #15784191, #15784206, #15784230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7156);