Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×#418 ⋊ C2 |
| Sylow | C3 ⋊ #10987 |
1466 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,c^b=cf,d^b=dh,d^c=dh,g^c=gh,i^c=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | #72248548, #72248563, #72248593, … |
| maximal normal subgroup of | #72248548, #72248563, #72248593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76156);