Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#6470 |
| Fitting | C4×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C4×#131 |
572 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13244467, #13244472, #13244477, … |
| maximal normal subgroup of | #13244467, #13244472, #13244477, … |
| maximal quotient of | C8×#6470, #13319409, #13319459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10726);