Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×#261 |
| Fitting | C13×2−1+4 ⋊ C4 |
| Sylow | C13 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#454, #261×#456, #16799815, … |
| maximal normal subgroup of | #261×#454, #261×#456, #16799815, … |
| maximal quotient of | #261×#520, #261×#519, #261×#536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21492);