Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#713 |
| Fitting | C2×C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×#41 |
| Sylow | C5 ⋊ C2×C7×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C7 | C22×D5 |
| commutator, cosocle | C2×C5 | C24×C7 |
| Frattini | C2 | C23×C7×D5 |
| Fitting | C2×C5×C7×Q8 | C2 |
| socle | C22×C5×C7 | C23 |
| hypercenter | C2×C7×Q8 | D5 |
| hypocenter | C5 | C2×C7×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C7×Q8 | |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1050);