Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#537 ⋊ C2 |
| Sylow | C7 ⋊ #3013 |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,h^b=h^6,d^c=dg98 conjugacy classes — view the full character table.
| maximal subgroup of | #13385254, #13385257, #13385263, … |
| maximal normal subgroup of | #13385254, #13385257, #13385263, … |
| maximal quotient of | #13327008, #13327019, #13327096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15638);