Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#356 ⋊ C2 |
| Sylow | C7 ⋊ #1410 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^7,7|a^2=d,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cfg,d^b=def,e^b=eg,h^b=h^6,d^c=dfg,e^d=eg56 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1410, C2×#11725358, #13274126, … |
| maximal normal subgroup of | D7×#1410, C2×#11725358, #13274126, … |
| maximal quotient of | #13241178, #13241212, #13241308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 124);