Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#393⋊C3 |
| unambiguous semidirect product | #393⋊(C3×C5) |
| unambiguous semidirect product | (C5×#393)⋊C3 |
| Fitting, Hall | C5×#393 ⋊ C3 |
| derived | C22×Q8 ⋊ C2×C3×C5 |
| Sylow | #393 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #120⋊C3 |
| commutator, cosocle, hypocenter | C22×Q8 | C2×C3×C5 |
| Frattini | C23 | C2×C5×A4 |
| Fitting | C5×#393 | C3 |
| socle | C23×C5 | C2×A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2×C5 | |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7)(8,11,12,10,9,13)(15,16,18)(19,21,20);(7,13)(10,11)(14,18,17,20)(15,21,19,16)90 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68001, C5×#72998, C5×#72999, … |
| maximal normal subgroup of | C5×#68001, C5×#72998, C5×#72999, … |
| maximal quotient of | C5×#1446⋊C3, C5×#2029⋊C3, C5×#2030⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3728);