Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#389 ⋊ C2 |
| Sylow | C7 ⋊ #2065 |
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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=d,b^2=deg,e^2=g,f^2=g,b^a=bdeg,c^a=ce,e^a=eg,f^a=fg,c^b=cf,h^b=h^6,e^c=eg,f^c=fg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2065, C2×#11727383, #13382411, … |
| maximal normal subgroup of | D7×#2065, C2×#11727383, #13382411, … |
| maximal quotient of | #13258310, #13258331, #13258366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2149);