Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×Q82 ⋊ C2 |
| Sylow | C7 ⋊ #3522 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×Q82 | C2 |
| hypercenter | Q82 | D7 |
| hypocenter | C7 | #3522 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^6,d^b=df,h^c=h^6,h^e=h^6119 conjugacy classes — view the full character table.
| maximal subgroup of | #13330265, #13330276, #13330353, … |
| maximal normal subgroup of | #13330265, #13330276, #13330353, … |
| maximal quotient of | #13514032, #13514557, #13514661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18877);