Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2280 ⋊ C2 |
| Sylow | C3 ⋊ #10994 |
1494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,c^b=cf,d^b=dh,e^b=eh,i^b=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72248346, #72248356, #72248364, … |
| maximal normal subgroup of | #72248346, #72248356, #72248364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76192);