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) = C22 |
| direct product | C2×#91166 |
| Hall | C3×C5 ⋊ C2×M32 |
| Sylow | C5 ⋊ C2×#798 |
| Sylow | C3 ⋊ C2×#3990 |
180 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C4×#91166, #14312621, #14312623, … |
| maximal normal subgroup of | C4×#91166, #14312621, #14312623, … |
| maximal quotient of | C2×#11746543, C4×#91166, C2×#11746547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5939);