Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#6411 |
| Sylow | C7 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6411, #13244507, #13244509, … |
| maximal normal subgroup of | C8×#6411, #13244507, #13244509, … |
| maximal quotient of | C4×D4⋊(C7⋊C8), C4×Q8⋊(C7⋊C8), #13244408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4162);