Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×#261 |
| unambiguous semidirect product | D13⋊(C4×Q16) |
| Fitting | C2×C13×Q16 ⋊ C4 |
| Sylow | C13 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#358, #16789498, #261×#362, … |
| maximal normal subgroup of | #261×#358, #16789498, #261×#362, … |
| maximal quotient of | C2×Q16×#1057, C2×#13130423, Q16×D13⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21259);