Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C4×C8 ⋊ D3 |
375 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 375 conjugacy classes of subgroups — too many to draw. Only its 49 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=c,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^2,h^a=hi,h^g=i,i^g=hi88 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D4⋊C8, #72342692, #72342714 |
| maximal normal subgroup of | S4×D4⋊C8, #72342692, #72342714 |
| maximal quotient of | #72342736, #72342865 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085526);