Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#89666 |
| Fitting | C2×C7×#108 ⋊ C2 |
| Sylow | C7 ⋊ C2×#444 |
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13269086, #13269088, #13269093, … |
| maximal normal subgroup of | #13269086, #13269088, #13269093, … |
| maximal quotient of | C2×#11726312, C2×#11726271, C2×#11726272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11459);