Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #1908 |
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=dfg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^6,d^b=dg,e^b=eg,f^b=fg,d^c=dg,e^c=eg,f^c=fg152 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1908, C2×#11729773, #13355731, … |
| maximal normal subgroup of | D7×#1908, C2×#11729773, #13355731, … |
| maximal quotient of | #13249270, #13249284, #13249633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4539);