Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#431 ⋊ C2 |
| Sylow | C13 ⋊ #3208 |
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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,h^a=h^12,c^b=ce,f^c=fg,h^c=h^12272 conjugacy classes — view the full character table.
| maximal subgroup of | #15759470, #15759472, #15759610, … |
| maximal normal subgroup of | #15759470, #15759472, #15759610, … |
| maximal quotient of | #15872225, #15872599, #15873434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15453);