Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×C7⋊C8 |
| Sylow | C7 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 333 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #101×C7⋊C8, #13244362, #13244371, … |
| maximal normal subgroup of | #101×C7⋊C8, #13244362, #13244371, … |
| maximal quotient of | C2×C4⋊C4×C7⋊C8, C4×Q8×C7⋊C8, C2×#11727236, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14643);