Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×#1161 |
| Fitting | C7×C8×Q8 ⋊ C2 |
| Sylow | C7 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13263627, #13263637, #13263667, … |
| maximal normal subgroup of | #13263627, #13263637, #13263667, … |
| maximal quotient of | C8×#6455, C8×#6456, C8×Q8×Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12113);