Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ #2947 |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^6,e^b=eg,h^b=h^6,d^c=dg164 conjugacy classes — view the full character table.
| maximal subgroup of | #13374588, #13374592, #13374606, … |
| maximal normal subgroup of | #13374588, #13374592, #13374606, … |
| maximal quotient of | #13323247, #13323438, #13323459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10782);