Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718555 |
| Fitting | C2×C13×#108 ⋊ C2 |
| Sylow | C13 ⋊ C2×#444 |
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #15778209, #15778211, #15778216, … |
| maximal normal subgroup of | #15778209, #15778211, #15778216, … |
| maximal quotient of | C2×#13113647, C2×#13113654, C2×#13113659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13405);