Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#419 ⋊ C2 |
| Sylow | C7 ⋊ #3011 |
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^6,e^b=eg,d^c=dg,h^c=h^698 conjugacy classes — view the full character table.
| maximal subgroup of | #13385322, #13385328, #13391213, … |
| maximal normal subgroup of | #13385322, #13385328, #13391213, … |
| maximal quotient of | #13326992, #13327080, #13327167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11172);