Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11718354 |
| Fitting | C2×C4×C8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15758207, #15758212, #15762151, … |
| maximal normal subgroup of | #15758207, #15758212, #15762151, … |
| maximal quotient of | C2×#13114423, C2×#13114428, C2×#13114433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14917);