Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×#107 ⋊ D3 |
621 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3,2^2|b^2=ef,c^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=hi,c^b=cef,e^c=ef,h^g=i,i^g=hi70 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D8×S4, #72342790, #72342792 |
| maximal normal subgroup of | C4×D8×S4, #72342790, #72342792 |
| maximal quotient of | #72342735, #72342792 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087513);