Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1722 |
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^6,c^b=cf,h^b=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1722, C2×#11728949, #13341585, … |
| maximal normal subgroup of | D7×#1722, C2×#11728949, #13341585, … |
| maximal quotient of | #13247587, #13253595, #13253598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3715);