Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting, Sylow | #62654 ⋊ C3 |
1997 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 1997 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
3,2^8|b^2=i,g^2=h,b^a=bei,c^a=di,d^a=cdhi,e^a=fh,f^a=efi,c^b=ch,g^b=gh,f^c=fh,e^d=eh70 conjugacy classes — view the full character table.
| maximal subgroup of | #72221904, #72227310, #72227324, … |
| maximal normal subgroup of | #72227310, #72227324, #72227325, … |
| maximal quotient of | #72221904 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084985);