Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2010 ⋊ C2 |
| Sylow | C3 ⋊ #30434 |
1000 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|e^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,g^a=gh,c^b=cg,d^b=de,e^b=eh,f^b=fh,e^d=eh,i^d=i^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#30434, C2×#10909601 |
| maximal normal subgroup of | D3×#30434, C2×#10909601 |
| maximal quotient of | C2×#10909601, #72248358, #72248394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 283982);