Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#436 ⋊ C2 |
| Sylow | C7 ⋊ #1594 |
176 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 63 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=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^6,c^b=cg,d^b=df116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1594, C2×#11728615, #13323568, … |
| maximal normal subgroup of | D7×#1594, C2×#11728615, #13323568, … |
| maximal quotient of | #13244628, #13244632, #13245056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3381);