Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C7×#339 ⋊ C2 |
| Sylow | C7 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^6140 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D7×#104, C2×#11726482, #13351517, … |
| maximal normal subgroup of | C4×D7×#104, C2×#11726482, #13351517, … |
| maximal quotient of | #13244387, #13244392, #13244407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1248);