Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#89484 |
| Fitting | C2×C7×#97 ⋊ C2 |
| Sylow | C7 ⋊ C2×#496 |
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #13248724, #13255076, #13255077, … |
| maximal normal subgroup of | #13248724, #13255076, #13255077, … |
| maximal quotient of | C2×#11725844, C2×#11725845, C2×#11725846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10709);