Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×#261 |
| Fitting | C13×H(5,𝔽2) ⋊ C4 |
| Sylow | C13 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1660 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) = 104 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#453, #261×#455, #16799813, … |
| maximal normal subgroup of | #261×#453, #261×#455, #16799813, … |
| maximal quotient of | #261×#518, #261×#520, #261×#534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21491);