Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C4 |
| direct product | Dic5×C42⋊C3 |
| unambiguous semidirect product | (C42×Dic5)⋊C3 |
| derived | C42×C5 ⋊ C3×C4 |
| Hall | C42×Dic5 ⋊ C3 |
| Sylow | C5 ⋊ C4×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C42⋊C3 |
| commutator, hypocenter | C42×C5 | C3×C4 |
| Frattini | C23 | D5×A4 |
| Fitting, cosocle | C2×C42×C5 | C2×C3 |
| socle | C23×C5 | C2×A4 |
| prime radical | C2×C5×C42⋊C3 | C2 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 ◁ C2 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #14511583, #170×C42⋊C3, #10604190⋊C3, … |
| maximal normal subgroup of | #14511583, #170×C42⋊C3, #10604190⋊C3, … |
| maximal quotient of | #168×C42⋊C3, Dic5×#95⋊C3, #10600227⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 804);