Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=e,e^2=f,b^a=bd,g^b=g^166,g^c=g^1661700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322930, #36322932, #36322935, … |
| maximal normal subgroup of | #36322930, #36322932, #36322935, … |
| maximal quotient of | #36322932, #36322937, #36322944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 614);