Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D167)⋊C8 |
| Fitting | C22⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D4×D167, C2×(C22⋊D167)⋊C8, #36332828, … |
| maximal normal subgroup of | C8×D4×D167, C2×(C22⋊D167)⋊C8, #36332828, … |
| maximal quotient of | #36322930, #36322935, #36322941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 612);