Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10587987 |
| Fitting | C22×C4×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×#41 |
| Sylow | C7 ⋊ C2×#709 |
| Sylow | C5 ⋊ C2×#1157 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D35 |
| commutator, cosocle | C2×C5×C7 | C24 |
| Frattini | C2 | C23×D35 |
| Fitting | C22×C4×C5×C7 | C2 |
| socle | C22×C5×C7 | C23 |
| hypercenter | C22×C4 | D35 |
| hypocenter | C5×C7 | C2×#41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1060);