Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581933, #36322417, #36322420, … |
| maximal normal subgroup of | C8×#14581933, #36322417, #36322420, … |
| maximal quotient of | #36323883, C4×(C2×D167)⋊C8, C4×Dic167⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 600);