Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#1131 |
| Fitting | C7×C8×Q8 ⋊ C2 |
| Sylow | C7 ⋊ Q8×M16 |
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13324714, #13324720, #13324725, … |
| maximal normal subgroup of | #13324714, #13324720, #13324725, … |
| maximal quotient of | C4⋊C4×#1131, #13352443, Q8×#6389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12130);