Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#6409 |
| Sylow | C7 ⋊ C22×#103 |
816 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13259365, #13259367, #13260063, … |
| maximal normal subgroup of | #13259365, #13259367, #13260063, … |
| maximal quotient of | C22×Q8⋊(C7⋊C8), C2×#11729376, C2×#11729578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 16266);