Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C4⋊C8 ⋊ D3 |
624 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,c^2=d,d^2=f,b^a=be,g^a=g^2,h^a=hi,c^b=ce,h^g=i,i^g=hi100 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D4×S4, #72342692, #72342704 |
| maximal normal subgroup of | C8×D4×S4, #72342692, #72342704 |
| maximal quotient of | #72342704, #72342879 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087493);