Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C29 |
| direct product | D5×C22⋊(C22⋊A4) |
| unambiguous semidirect product | C5⋊(C2×C22⋊(C22⋊A4)) |
| Fitting, socle, derived | C26×C5 ⋊ C2×C3 |
| Hall | C26×D5 ⋊ C3 |
| Sylow | C5 ⋊ C2×C22⋊(C22⋊A4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C26×C5 | C2×C3 |
| LCS | G ▷ C26×C5 | |
| UCS | C1 | |
19768 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C22⋊(C22⋊A4), D5×#87588, #72246556, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C22⋊(C22⋊A4), D5×#87588, #72246556, … |
| maximal quotient of | D5×C22⋊#997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240416);