Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #1441 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D7 |
| commutator | C23×C7 | C22×C4 |
| Fitting | C22×C7×C4⋊C4 | C2 |
| socle, prime radical, cosocle | C24×C7 | C23 |
| hypercenter | C22×C4⋊C4 | D7 |
| hypocenter | C7 | #1441 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=d,c^2=d,b^a=bd,c^a=ce,h^a=h^6,c^b=cf164 conjugacy classes — view the full character table.
| maximal subgroup of | #13240919, #13240920, #13245602, … |
| maximal normal subgroup of | #13240919, #13240920, #13245602, … |
| maximal quotient of | #13241720, #13241723, #13241724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4085);