Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3255 |
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^6,c^b=ceg,f^c=fg110 conjugacy classes — view the full character table.
| maximal subgroup of | #13255310, #13255312, #13255313, … |
| maximal normal subgroup of | #13255310, #13255312, #13255313, … |
| maximal quotient of | #13363748, #13363752, #13364194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15585);