Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #1839 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D7 |
| commutator | C22×C7 | C22×C8 |
| Fitting | C43×C7 | C2 |
| socle, prime radical | C23×C7 | C22×C4 |
| cosocle | C22×C4×C7 | C23 |
| hypercenter | C43 | D7 |
| hypocenter | C7 | #1839 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^6248 conjugacy classes — view the full character table.
| maximal subgroup of | #13240331, #13240332, #13240342, … |
| maximal normal subgroup of | #13240331, #13240332, #13240342, … |
| maximal quotient of | #13247516, #13247520, #13259401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1913);