Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #10716 |
1414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,d^2=h,b^a=bd,c^a=ce,g^a=gh,f^b=fh,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72248329, #72248335, #72248356, … |
| maximal normal subgroup of | #72248329, #72248335, #72248356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 74798);