Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#19128807 |
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#121 |
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 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 | #36324454, #36324459, #36324565, … |
| maximal normal subgroup of | #36324454, #36324459, #36324565, … |
| maximal quotient of | C2×#24923126, C2×#24923147, C2×#24923161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1042);