Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#405 ⋊ C2 |
| Sylow | C7 ⋊ #1931 |
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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|a^2=f,b^2=dfg,c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^6,e^c=eg152 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1931, C2×#11727646, #13356339, … |
| maximal normal subgroup of | D7×#1931, C2×#11727646, #13356339, … |
| maximal quotient of | #13252032, #13252046, #13252123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2412);