Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#89676 |
| Fitting | C22×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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) = 448 |
236 conjugacy classes — view the full character table.
| maximal subgroup of | #13270845, #13270847, #13270880, … |
| maximal normal subgroup of | #13270845, #13270847, #13270880, … |
| maximal quotient of | C2×#11729166, C2×#11729158, C2×C4×D112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14214);