Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10587859 |
| Hall | C5×C7 ⋊ C2×C4⋊C4 |
| Sylow | C7 ⋊ C2×#683 |
| Sylow | C5 ⋊ C2×C4⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D7 |
| commutator | C2×C5×C7 | C22×C4 |
| Frattini | C22 | C2×D5×D7 |
| Fitting, socle, prime radical | C23×C5×C7 | C22 |
| cosocle | C22×C5×C7 | C23 |
| hypocenter | C5×C7 | C2×C4⋊C4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C23 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 595);