Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#89292 |
| Fitting | C2×C7×#108 ⋊ C2 |
| Sylow | C7 ⋊ C2×#359 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13269019, C4×#89292, #13269024, … |
| maximal normal subgroup of | #13269019, C4×#89292, #13269024, … |
| maximal quotient of | C2×#11725277, C2×#11725278, #13263534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3209);