Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #11757174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11757174 |
| unambiguous semidirect product | D5⋊#5936 |
| Fitting, socle | C25×C5 ⋊ Dic3 |
| derived | C5×C22⋊A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×#5936 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757174 |
| commutator, hypocenter | C5×C22⋊A4 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | Dic3 |
| prime radical | C2×D5×C22⋊A4 | C2 |
| cosocle | D5×C22⋊A4 | C22 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
1694 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 1694 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #72221428, #72221473, #72222068, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#1020, AGL(1,𝔽5)×#5936, #72242734, … |
| maximal quotient of | #72221428, #72221473, C2×#14514395, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240404);