Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×C7⋊C8 |
| Sylow | C7 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #99×C7⋊C8, #13244340, #13244344, … |
| maximal normal subgroup of | #99×C7⋊C8, #13244340, #13244344, … |
| maximal quotient of | C2×D8×C7⋊C8, C2×SD16×C7⋊C8, C2×Q16×C7⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14508);