Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#460 ⋊ C2 |
| Sylow | C7 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^6,e^d=eg,h^d=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | #13343153, #13343161, #13343168, … |
| maximal normal subgroup of | #13343153, #13343161, #13343168, … |
| maximal quotient of | #13343270, #13343285, #13343300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12617);