Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×Q32 ⋊ C2 |
| Sylow | C7 ⋊ #2264 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^6,d^b=de,e^b=ef,f^b=fg92 conjugacy classes — view the full character table.
| maximal subgroup of | #13274412, #13274417, #13274472, … |
| maximal normal subgroup of | #13274412, #13274417, #13274472, … |
| maximal quotient of | #13274233, #13274243, #13274301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4013);