Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C167 ⋊ C2 |
| Sylow | C167 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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,c^2=f,d^2=e,b^a=be,g^c=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323942, #36323947, #36324157, … |
| maximal normal subgroup of | #36323942, #36323947, #36324157, … |
| maximal quotient of | #36326477, #117×Dic167, C4×(C22⋊D167)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1017);