Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2101 |
198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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=de,c^2=dg,f^2=g,b^a=bdg,c^a=ceg,h^a=h^6,c^b=cf,f^b=fg,f^c=fg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2101, C2×#11726599, #13383708, … |
| maximal normal subgroup of | D7×#2101, C2×#11726599, #13383708, … |
| maximal quotient of | #13258934, #13261710, #13262061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1365);