Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×#1159 |
| Fitting | C5×C7×D4 ⋊ C22 |
| Hall | C5×C7 ⋊ C2×#41 |
| Sylow | C7 ⋊ D5×#41 |
| Sylow | C5 ⋊ C2×#1159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×D7 |
| commutator, socle, cosocle | C2×C5×C7 | C24 |
| Fitting | C5×C7×D4 | C22 |
| hypercenter | D4 | D5×D7 |
| hypocenter | C5×C7 | C2×#41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ D4 | |
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1159⋊C3, D5×#6474, #72218327, … |
| maximal normal subgroup of | D5×#1159⋊C3, D5×#6474, #72218327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1000);