Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128810 |
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322500, C4×#19128810, #36326672, … |
| maximal normal subgroup of | #36322500, C4×#19128810, #36326672, … |
| maximal quotient of | C2×#24923128, C2×#24923140, C2×#24923143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1046);