Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C5⋊#857 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×C5⋊#857 |
| unambiguous semidirect product | (C2×C5)⋊#857 |
| Fitting | C2×C42×C5 ⋊ D3 |
| derived | C5×C42⋊C3 ⋊ C22 |
| Sylow | C5 ⋊ C2×#857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#857 |
| commutator, cosocle, hypocenter | C5×C42⋊C3 | C22 |
| Frattini | C22 | C2×C5⋊S4 |
| Fitting | C2×C42×C5 | D3 |
| socle | C23×C5 | S4 |
| LCS | G ▷ C5×C42⋊C3 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #14511628, #14511629, #14511630, … |
| maximal normal subgroup of | #14511628, #14511629, #14511630, … |
| maximal quotient of | #14511894, C4×C5⋊#857, C4⋊(C5⋊#857), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6299);