Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C2×D5×C42⋊C3 |
| unambiguous semidirect product | C5⋊(C22×C42⋊C3) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C42⋊C3) |
| unambiguous semidirect product | (C2×C42×D5)⋊C3 |
| Fitting | C2×C42×C5 ⋊ C2×C3 |
| derived | C42×C5 ⋊ C22×C3 |
| Hall | C2×C42×D5 ⋊ C3 |
| Sylow | C5 ⋊ C22×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C42⋊C3 |
| commutator, cosocle, hypocenter | C42×C5 | C22×C3 |
| Frattini | C22 | C2×D5×A4 |
| Fitting | C2×C42×C5 | C2×C3 |
| socle | C23×C5 | C2×A4 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 ◁ C2 | |
216 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 28 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 | D5×#4623, #14511634, #14511636, … |
| maximal normal subgroup of | D5×#4623, #14511634, #14511636, … |
| maximal quotient of | Dic10×C42⋊C3, C4×D5×C42⋊C3, D20×C42⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6349);