Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ #433 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,c^2=d,e^2=f,b^a=bd,c^b=cf,g^b=g^1662684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #433×D167, C2×#24923328, #36332772, … |
| maximal normal subgroup of | #433×D167, C2×#24923328, #36332772, … |
| maximal quotient of | #36323889, #36323905, #36323996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 608);