Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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,b^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^1661187 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36335645, #36335646, #36335652, … |
| maximal normal subgroup of | #36335645, #36335646, #36335652, … |
| maximal quotient of | #36326970, #36326972, #36327034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1212);