Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6118 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×D13⋊M16 |
| unambiguous semidirect product | D13⋊(C22×M16) |
| Sylow | C13 ⋊ C23×M16 |
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16785260, #16785268, #16785271, … |
| maximal normal subgroup of | #16785260, #16785268, #16785271, … |
| maximal quotient of | C22×#11719047, C22×C4×#6122, C2×C4×D13⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21496);