Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C5⋊((C22⋊C9)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×(C22⋊C9)⋊Dic5 |
| unambiguous semidirect product | (C2×C22⋊C9)⋊Dic5 |
| derived | C5×C22⋊C9 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×(C22⋊C9)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C5⋊((C22⋊C9)⋊C2) |
| commutator, hypocenter | C5×C22⋊C9 | C2×C4 |
| Frattini | C2×C3 | C2×C5⋊S4 |
| Fitting, socle, prime radical | C24×C3×C5 | D3 |
| cosocle | C2×C5×C22⋊C9 | C22 |
| LCS | G ▷ C5×C22⋊C9 | |
| UCS | C1 ◁ C22 | |
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1529);