Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D7 |
| commutator | C2×C7 | C82 |
| Fitting | C7×C82 | C2 |
| socle, prime radical | C22×C7 | C4×C8 |
| cosocle | C4×C7×C8 | C22 |
| hypercenter | C82 | D7 |
| hypocenter | C7 | #1311 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4×C8 ◁ C82 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^a=h^6272 conjugacy classes — view the full character table.
| maximal subgroup of | #13240413, #13240462, #13240463, … |
| maximal normal subgroup of | #13240413, #13240462, #13240463, … |
| maximal quotient of | #13240411, #13240624, #13241126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 9);