Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ #2636 |
562 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 562 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) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^12272 conjugacy classes — view the full character table.
| maximal subgroup of | #15836339, #15836343, #15836369, … |
| maximal normal subgroup of | #15836339, #15836343, #15836369, … |
| maximal quotient of | #15789373, #15789403, #15789591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 10405);