Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#383⋊C3 |
| unambiguous semidirect product | #383⋊(C3×C5) |
| unambiguous semidirect product | (C5×#383)⋊C3 |
| Fitting, Hall | C5×#383 ⋊ C3 |
| derived | C42 ⋊ C3×C4×C5 |
| Sylow | #383 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #126⋊C3 |
| commutator, hypocenter | C42 | C3×C4×C5 |
| Frattini | C23 | C2×C5×A4 |
| Fitting | C5×#383 | C3 |
| socle | C23×C5 | C2×A4 |
| prime radical | C2×C5×C42⋊C3 | C2 |
| cosocle | C2×C42 | C2×C3×C5 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C5 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5)(6,7,8,9)(11,19,20,15,12,22)(13,14,16)(17,18,21,25,23,24);(10,22,14,25)(11,19,18,12)(13,17,16,20)(15,24,23,21)100 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×#383⋊C3, C4×C5×#126⋊C3, C5×#2380⋊C3, … |
| maximal normal subgroup of | C2×C5×#383⋊C3, C4×C5×#126⋊C3, C5×#2380⋊C3, … |
| maximal quotient of | C5×#1443⋊C3, C5×#1839⋊C3, C5×#1840⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3725);