Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#89278 |
| Fitting | C2×C7×C4⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ C2×D4⋊C8 |
344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13244387, C4×#89278, #13244397, … |
| maximal normal subgroup of | #13244387, C4×#89278, #13244397, … |
| maximal quotient of | C2×#11725285, C2×#11725284, #13241736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2944);