Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | A4×#713 |
| Fitting | C22×C5×Q8 ⋊ C2×C3 |
| Hall | C22×#713 ⋊ C3 |
| Sylow | C5 ⋊ A4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C23×C3 |
| Fitting | C22×C5×Q8 | C2×C3 |
| hypercenter | Q8 | D5×A4 |
| hypocenter | C22×C5 | C3×#41 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
430 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #14512491, A4×#4010, #14513245, … |
| maximal normal subgroup of | #14512491, A4×#4010, #14513245, … |
| maximal quotient of | A4×#4036, A4×#4038, A4×#4039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11133);