Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2960 |
364 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 364 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) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^c=h^12224 conjugacy classes — view the full character table.
| maximal subgroup of | #15753926, #15753936, #15753948, … |
| maximal normal subgroup of | #15753926, #15753936, #15753948, … |
| maximal quotient of | #15860866, #15860889, #15861528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13440);