Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×C5×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | C42 |
| commutator | C4 | C3×C42×C5 |
| Frattini, cosocle | C22×C4 | C22×C3×C5 |
| socle | C2×C3×C5 | #95 |
| prime radical | C23×C3×C5 | D4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ G | |
188 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,6,7,8)(9,10)(11,17,19,23)(12,15)(13,16)(14,18,21,24)(20,22);(9,11)(10,14,16,21)(12,18)(13,19)(15,17,22,23)(20,24)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 600);