Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C3×#388 ⋊ C2 |
| Sylow | C3 ⋊ #14444 |
1658 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=h,b^2=ef,c^2=efg,d^2=f,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,i^c=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 98020);