Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic7⋊#170 |
| Hall | C5×C7 ⋊ C4⋊C8 |
| Sylow | C7 ⋊ C4⋊#170 |
| Sylow | C5 ⋊ Dic7⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D7×AGL(1,𝔽5) |
| commutator | C2×C5×C7 | C2×C8 |
| Fitting, socle, prime radical | C22×C5×C7 | C2×C4 |
| cosocle | C2×C7×Dic5 | C22 |
| hypocenter | C5×C7 | C4⋊C8 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
Polycyclic presentation:
2^5,5,7|a^2=d,b^2=c,c^2=e,b^a=bd,g^a=g^6,f^b=f^2,f^c=f^488 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 245);