Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊#261 |
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783589, #16783590, #16783597, … |
| maximal normal subgroup of | #16783589, #16783590, #16783597, … |
| maximal quotient of | C4⋊C4×C22⋊#261, Q8×(C2×#261)⋊C4, #16791649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21014);