Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×D4×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #3373 |
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^6,c^b=cg,d^b=de,f^c=fg104 conjugacy classes — view the full character table.
| maximal subgroup of | #13343649, #13343651, #13343709, … |
| maximal normal subgroup of | #13343649, #13343651, #13343709, … |
| maximal quotient of | #13370432, #13370639, #13372758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15780);