Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #23900 |
3520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|b^a=be,c^a=cf,d^a=de,c^b=cg,f^b=fh,i^b=i^2,e^c=eh,f^d=fh78 conjugacy classes — view the full character table.
| maximal subgroup of | #72214841, D3×#23900, #72219817, … |
| maximal normal subgroup of | D3×#23900, #72219817, #72231044, … |
| maximal quotient of | #72214841, #72231591, #72245154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 201146);