Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#525 ⋊ C2 |
| Sylow | C7 ⋊ #3194 |
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^c=h^6110 conjugacy classes — view the full character table.
| maximal subgroup of | #13250752, #13250754, #13327950, … |
| maximal normal subgroup of | #13250752, #13250754, #13327950, … |
| maximal quotient of | #13362866, #13362886, #13364085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15142);