Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C5×#419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D4 |
| commutator | C4 | C22×C3×C4×C5 |
| Frattini, cosocle | C2×C4 | C23×C3×C5 |
| prime radical | C23×C3×C5 | D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
300 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14)(15,22)(16,20)(17,26)(18,21)(19,24)(23,27)(25,28);(13,15,18,25)(14,19,21,27)(16,24,17,23)(20,28,26,22);(13,16,18,17)(14,20,21,26)(15,23,25,24)(19,22,27,28)330 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5589);