Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#461 ⋊ C2 |
| Sylow | C7 ⋊ #1701 |
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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|b^2=dfg,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^6,e^c=eg80 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1701, C2×#11728797, #13336379, … |
| maximal normal subgroup of | D7×#1701, C2×#11728797, #13336379, … |
| maximal quotient of | #13246908, #13250007, #13250031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3563);