Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #459 |
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^166,e^c=ef1181 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #459×D167, C2×#24923462, #36333589, … |
| maximal normal subgroup of | #459×D167, C2×#24923462, #36333589, … |
| maximal quotient of | #36323477, #36323481, #36323491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 742);