Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C3×C4×#121 ⋊ C2 |
| Sylow | C3 ⋊ #34415 |
2766 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=fh,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^b=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#34415, #72254326, #72254357 |
| maximal normal subgroup of | D3×#34415, #72254326, #72254357 |
| maximal quotient of | #72253490 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 333085);