Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×A4×#41 |
| Fitting, Hall | C22×C5×#41 ⋊ C3 |
| Sylow | C22×#41 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×A4 |
| commutator, cosocle | C23 | C23×C3×C5 |
| Frattini | C2 | C23×C5×A4 |
| Fitting | C22×C5×#41 | C3 |
| socle | C23×C5 | C23×C3 |
| hypercenter | C5×#41 | A4 |
| hypocenter | C22 | C3×C5×#41 |
| LCS | G ▷ C23 ▷ C22 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73150, C5×A4×#104, C5×#85511, … |
| maximal normal subgroup of | C5×#73150, C5×A4×#104, C5×#85511, … |
| maximal quotient of | C5×A4×#117, C4×C5×D4×A4, C4×C5×Q8×A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11279);