Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C7×H(5,𝔽2) ⋊ C2 |
| Sylow | C7 ⋊ #3585 |
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^6,f^b=fg,d^c=dg143 conjugacy classes — view the full character table.
| maximal subgroup of | #13385090, #13385091, #13385112, … |
| maximal normal subgroup of | #13385090, #13385091, #13385112, … |
| maximal quotient of | #14217367, #14217379, #14217480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19111);