Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of #63305 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#63307 |
| Hall | C5×C7 ⋊ C22×D4 |
| Sylow | C7 ⋊ C22×D20 |
| Sylow | C5 ⋊ C22×C22⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D7 |
| commutator, cosocle | C2×C5×C7 | C24 |
| Frattini | C2 | C22×D5×D7 |
| Fitting, socle | C23×C5×C7 | C22 |
| hypocenter | C5×C7 | C22×D4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C23 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1021);