Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ #2094 |
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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,d^2=g,e^2=g,b^a=bdg,c^a=ceg,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg,h^c=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2094, C2×#11728341, #13383590, … |
| maximal normal subgroup of | D7×#2094, C2×#11728341, #13383590, … |
| maximal quotient of | #13258776, #13258805, #13258837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3107);