Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | M16×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C4 | C22×A5 |
| commutator, socle | C2×A5 | C2×C4 |
| Fitting, hypercenter | M16 | A5 |
| prime radical | C22×A5 | C4 |
| hypocenter | A5 | M16 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C4 ◁ M16 | |
151 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | #14514736, #100×A5, #14514739, … |
| maximal normal subgroup of | #14514736, #100×A5, #14514739, … |
| maximal quotient of | #97×A5, C22⋊C8×A5, C4⋊C8×A5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5737);