Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D7×#508 |
| Fitting | C7×#508 ⋊ C2 |
| Sylow | C7 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1417, #13274249, D7×#1418, … |
| maximal normal subgroup of | D7×#1417, #13274249, D7×#1418, … |
| maximal quotient of | D7×#2138, D7×#2158, C4×D7×D16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14240);