Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #13839 |
2702 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=h,d^2=e,b^a=be,c^a=cf,i^a=i^2,c^b=cg,i^c=i^2168 conjugacy classes — view the full character table.
| maximal subgroup of | #72270870, #72270885, #72270909, … |
| maximal normal subgroup of | #72270870, #72270885, #72270909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 91251);