Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#541 ⋊ C2 |
| Sylow | C13 ⋊ #3222 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3222, C2×#13125902, #16734324, … |
| maximal normal subgroup of | D13×#3222, C2×#13125902, #16734324, … |
| maximal quotient of | #15872287, #15872716, #15873502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15576);