Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C7×D8 ⋊ C2 |
| Sylow | C7 ⋊ #1999 |
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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|d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13265891, #13265896, #13265901, … |
| maximal normal subgroup of | #13265891, #13265896, #13265901, … |
| maximal quotient of | #13253989, #13253996, #13254017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4563);