Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ #390 |
258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,b^2=df,c^2=e,b^a=bd,c^a=ce,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #390×D167, C2×#24923169, #36326597, … |
| maximal normal subgroup of | #390×D167, C2×#24923169, #36326597, … |
| maximal quotient of | Dic167⋊#95, #36322374, #36322375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 449);