Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C167 ⋊ #376 |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36321966, #36322030, #36322032, … |
| maximal normal subgroup of | #36321966, #36322030, #36322032, … |
| maximal quotient of | C4×C167⋊#95, #36322363, #36322365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 395);