Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2333 |
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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=g,b^2=eg,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=ce284 conjugacy classes — view the full character table.
| maximal subgroup of | #15760963, #15760967, #15760977, … |
| maximal normal subgroup of | #15760963, #15760967, #15760977, … |
| maximal quotient of | #15784188, #15784254, #15784283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7275);