Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#535 ⋊ C2 |
| Sylow | C7 ⋊ #3199 |
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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,h^a=h^6,c^b=ce,d^b=dg,f^c=fg92 conjugacy classes — view the full character table.
| maximal subgroup of | #13272778, #13272780, #13272795, … |
| maximal normal subgroup of | #13272778, #13272780, #13272795, … |
| maximal quotient of | #13362889, #13362894, #13364107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15598);