Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#338 ⋊ C2 |
| Sylow | C7 ⋊ #2091 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,b^2=de,d^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^6,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | #13267122, #13267127, #13267133, … |
| maximal normal subgroup of | #13267122, #13267127, #13267133, … |
| maximal quotient of | #13258766, #13258773, #13258778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1241);