Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×C3×#4099 |
| Fitting | C25×C3×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#120 |
| Sylow | C5 ⋊ C2×C3×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C22×D5 |
| commutator, cosocle | C22×C5 | C24×C3 |
| Frattini | C22 | C23×C3×D5 |
| Fitting | C25×C3×C5 | C2 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C25×C3 | D5 |
| hypocenter | C5 | C2×C3×#120 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C3 ◁ C25×C3 | |
1324 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10600292, #14301644, C3×#10600289, … |
| maximal normal subgroup of | C3×#10600292, #14301644, C3×#10600289, … |
| maximal quotient of | C2×C3×#65536, C2×C3×#65499, C2×C3×#65502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10046);