Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718558 |
| Fitting | C2×C13×#108 ⋊ C2 |
| Sylow | C13 ⋊ C2×#472 |
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 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #15779883, #15779885, #15779946, … |
| maximal normal subgroup of | #15779883, #15779885, #15779946, … |
| maximal quotient of | C2×#13114192, C2×#13114236, C2×#13114246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14218);