Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C22×C5×ΓL(1,𝔽25) |
| Fitting | C22×C3×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ C22×M16 |
| Sylow | C3 ⋊ C22×C5×M16 |
596 conjugacy classes of subgroups; only the 334 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 334 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#68660, #14294316, C5×#68661, … |
| maximal normal subgroup of | C5×#68660, #14294316, C5×#68661, … |
| maximal quotient of | C22×C5×#815, C2×C4×C5×ΓL(1,𝔽25), C22×C5×(C2×D3)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10317);