Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #14134 |
4586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=h,c^2=fh,b^a=be,c^a=cf,d^a=de,c^b=cg,i^c=i^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #72248465, D3×#14134, #72248480, … |
| maximal normal subgroup of | #72248465, D3×#14134, #72248480, … |
| maximal quotient of | #72249292, #72249293 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 94544);