Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3164 |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=e,c^2=fg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13412698, #13412702, #13412709, … |
| maximal normal subgroup of | #13412698, #13412702, #13412709, … |
| maximal quotient of | #13354244, #13357159, #13357173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15684);