Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C167 ⋊ C2 |
| Sylow | C167 ⋊ #380 |
234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,167|a^2=f,b^2=d,b^a=bd,c^a=ce,g^b=g^166,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322678, #36322680, #36322704, … |
| maximal normal subgroup of | #36322678, #36322680, #36322704, … |
| maximal quotient of | (C2×D167)⋊#95, #36322363, Dic167⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 408);