Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C167 ⋊ C2 |
| Sylow | C167 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,g^a=g^166,e^b=ef,g^b=g^1661682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324499, #36324501, #36324638, … |
| maximal normal subgroup of | #36324499, #36324501, #36324638, … |
| maximal quotient of | #36332658, #36332728, #36332940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1349);