Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic35 |
| derived, Hall | C5×C7 ⋊ C2×C42 |
| Sylow | C7 ⋊ C2×C4×Dic5 |
| Sylow | C5 ⋊ C2×C4×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D35 |
| commutator, hypocenter | C5×C7 | C2×C42 |
| Frattini | C22 | C22×D35 |
| Fitting | C22×C4×C5×C7 | C2 |
| socle, prime radical | C23×C5×C7 | C22 |
| cosocle | C22×C5×C7 | C23 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C22×C4 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 858);