Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ #2280 |
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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|a^2=g,d^2=e,b^a=be,c^a=cf,h^c=h^6176 conjugacy classes — view the full character table.
| maximal subgroup of | #13259026, #13259030, #13259036, … |
| maximal normal subgroup of | #13259026, #13259030, #13259036, … |
| maximal quotient of | #13274893, #13274911, C4×#89727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14478);