Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718534 |
| Sylow | C13 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #15778127, #15778137, #15778176, … |
| maximal normal subgroup of | #15778127, #15778137, #15778176, … |
| maximal quotient of | C2×#13113642, C2×#13113685, C2×#13113732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13274);