Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C167 ⋊ #435 |
124 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 61 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=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^166,g^c=g^1661688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #435×D167, C2×#24923341, #36332827, … |
| maximal normal subgroup of | #435×D167, C2×#24923341, #36332827, … |
| maximal quotient of | #36322968, #36322975, #36322982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 621);