Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×A42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | D5×A42 |
| unambiguous semidirect product | C5⋊(C2×A42) |
| unambiguous semidirect product | (C22×D5×A4)⋊C3 |
| unambiguous semidirect product | (D5×C22⋊A4)⋊C3 |
| Fitting, socle, derived | C24×C5 ⋊ C2×C32 |
| Hall | C24×D5 ⋊ C32 |
| Sylow | C5 ⋊ C2×A42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C5 | C2×C32 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 | |
244 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | A42×AGL(1,𝔽5), D5×A4⋊S4, #72224624, … |
| maximal normal subgroup of | A42×AGL(1,𝔽5), D5×A4⋊S4, #72224624, … |
| maximal quotient of | D5×Ω+(4,𝔽3), A42×C5⋊D5, C2×D5×A42, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5878);