Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#92101 |
| Fitting | C2×C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×2−1+4 |
| Sylow | C5 ⋊ C2×#1010 |
| Sylow | C3 ⋊ C2×#4150 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D15 |
| commutator, cosocle | C2×C3×C5 | C25 |
| Frattini | C2 | C24×D15 |
| Fitting | C2×C3×C5×#41 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C2×#41 | D15 |
| hypocenter | C3×C5 | C2×2−1+4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
1588 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1588 conjugacy classes of subgroups — too many to draw. Only its 587 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | #14297221, #14297230, #14297240, … |
| maximal normal subgroup of | #14297221, #14297230, #14297240, … |
| maximal quotient of | C2×#11756331, C2×#11756275, C2×#11756305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11340);