Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#6406 |
| Sylow | C7 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 396 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 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6406, #13244563, #13244572, … |
| maximal normal subgroup of | C8×#6406, #13244563, #13244572, … |
| maximal quotient of | C4×D4⋊(C7⋊C8), #13244418, #13244433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4128);