Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#6510 |
| Fitting | C23×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ C22×#124 |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13246431, #13260337, #13260340, … |
| maximal normal subgroup of | #13246431, #13260337, #13260340, … |
| maximal quotient of | C22×#89749, C22×#89762, C22×#89760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19079);