Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #342 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,b^a=bc,c^a=cf,d^b=df,g^b=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #342×D137, C2×#22577169, #31780520, … |
| maximal normal subgroup of | #342×D137, C2×#22577169, #31780520, … |
| maximal quotient of | #31778631, #31778635, #31778637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 315);