Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #2315 |
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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,c^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 | #15769126, #15769128, #15769130, … |
| maximal normal subgroup of | #15769126, #15769128, #15769130, … |
| maximal quotient of | #15784173, #15784198, #15784202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7122);