Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C7×#108 ⋊ C2 |
| Sylow | C7 ⋊ #1978 |
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 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) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=df,c^2=eg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,f^b=fg,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13270886, #13270889, #13270893, … |
| maximal normal subgroup of | #13270886, #13270889, #13270893, … |
| maximal quotient of | #13252720, #13252730, #13252984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3229);