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×M16 ⋊ C2 |
| Sylow | C13 ⋊ #2921 |
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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=f,c^2=e,f^2=g,b^a=be,d^a=dg,c^b=cg,h^b=h^12284 conjugacy classes — view the full character table.
| maximal subgroup of | #15760261, #15760263, #15760266, … |
| maximal normal subgroup of | #15760261, #15760263, #15760266, … |
| maximal quotient of | #15860398, #15860467, #15860827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13146);