Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×C22⋊D167 |
| Fitting | C23×C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322454, #36322474, C4×#19128746, … |
| maximal normal subgroup of | #36322454, #36322474, C4×#19128746, … |
| maximal quotient of | C2×C4×C22⋊Dic167, C2×C4×(C2×D167)⋊C4, C2×C4×Dic167⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1008);