Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D3)⋊#170 |
| Hall | C3×C5 ⋊ C2×C22⋊C8 |
| Sylow | C5 ⋊ C2×(C2×D3)⋊C8 |
| Sylow | C3 ⋊ C2×C22⋊#170 |
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #14295027, C4×(C2×D3)⋊#170, #14295070, … |
| maximal normal subgroup of | #14295027, C4×(C2×D3)⋊#170, #14295070, … |
| maximal quotient of | C2×#11746566, C2×#11746568, #14280833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6193);