Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #2024 |
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^6,e^c=eg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2024, C2×#11726664, #13381090, … |
| maximal normal subgroup of | D7×#2024, C2×#11726664, #13381090, … |
| maximal quotient of | #13256770, #13256780, #13256810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1430);