Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D35 |
| Fitting, socle | C24×C5×C7 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C25 |
| Sylow | C7 ⋊ C24×D5 |
| Sylow | C5 ⋊ C24×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C5×C7 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C24 | |
1496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×D5×D7, C24×C5⋊AGL(1,𝔽7), #120×D35, … |
| maximal normal subgroup of | C24×D5×D7, C24×C5⋊AGL(1,𝔽7), #120×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1091);