Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ #23996 |
1396 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|b^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^2,c^b=cg,g^b=gh,i^b=i^2,e^c=eh,f^d=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#23996, #72231044, #72231088, … |
| maximal normal subgroup of | D3×#23996, #72231044, #72231088, … |
| maximal quotient of | #72270004, #72270458, C2×#10827757 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 202138);