Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic14 |
| Sylow | C7 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13248130, #13248134, #13248144, … |
| maximal normal subgroup of | #13248130, #13248134, #13248144, … |
| maximal quotient of | M16×C4⋊Dic7, M16×Dic7⋊C4, #13352445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10720);