Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D4×D167 |
| Fitting | C4×D4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D167, #36322527, #36322561, … |
| maximal normal subgroup of | D4⋊C8×D167, #36322527, #36322561, … |
| maximal quotient of | C4×C22⋊C4×D167, C4×C4⋊C4×D167, C4×(C22⋊D167)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1006);