Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#577⋊C3 |
| unambiguous semidirect product | #577⋊(C3×C5) |
| unambiguous semidirect product | (C5×#577)⋊C3 |
| Fitting, Hall | C5×#577 ⋊ C3 |
| Sylow | #577 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | D4×A4 |
| commutator, cosocle | #41 | C22×C3×C5 |
| Frattini | C4 | C22×C5×A4 |
| Fitting | C5×#577 | C3 |
| hypercenter | C5×SD16 | A4 |
| hypocenter | Q8 | C3×C5×D4 |
| LCS | G ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 ◁ C5×SD16 | |
146 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#85469, C5×#85470, C5×#85471, … |
| maximal normal subgroup of | C5×#85469, C5×#85470, C5×#85471, … |
| maximal quotient of | C5×#2897⋊C3, C5×#2898⋊C3, C5×#2912⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9665);