Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C5×C7 ⋊ C2×C16 |
| Sylow | C7 ⋊ D5⋊C16 |
| Sylow | C5 ⋊ D7×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D7×AGL(1,𝔽5) |
| commutator, hypocenter | C5×C7 | C2×C16 |
| Fitting | C4×C5×C7 | C2×C4 |
| socle | C2×C5×C7 | C2×C8 |
| prime radical | C2×D35 | C8 |
| cosocle | C7×#168 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C4 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=d,b^2=c,c^2=d,d^2=e,g^a=g^6,f^b=f^2,f^c=f^4100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 233);