Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#89826 |
| Sylow | C7 ⋊ C2×#464 |
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
122 conjugacy classes — view the full character table.
| maximal subgroup of | #13250135, #13250141, C4×#89826, … |
| maximal normal subgroup of | #13250135, #13250141, C4×#89826, … |
| maximal quotient of | C2×#11728962, C2×#11728994, C2×#11728963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15159);