Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×C7⋊C16 |
| Sylow | C7 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13265559, SD16×C7⋊C16, #13265573, … |
| maximal normal subgroup of | #13265559, SD16×C7⋊C16, #13265573, … |
| maximal quotient of | C4⋊C4×C7⋊C16, #13271413, #13271797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3468);