Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #66054⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #66054⋊C3 |
| Fitting | C5×#127 ⋊ C2×C3 |
| derived | C42×C5 ⋊ C22×C3 |
| Hall | #66054 ⋊ C3 |
| Sylow | C5 ⋊ #560⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C42×C5 | C22×C3 |
| Frattini | C22 | C2×D5×A4 |
| Fitting | C5×#127 | C2×C3 |
| socle | C22×C5 | C22×A4 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 | |
134 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^2,3,2^2,5,2^2|d^2=h,e^2=g,d^a=dgh,e^a=eh,f^a=f^4,d^b=dh,e^b=eg,d^c=de,e^c=dg,g^c=h,h^c=gh37 conjugacy classes — view the full character table.
| maximal subgroup of | (#857⋊C2)⋊D5, #4626⋊D5, C2×#66054⋊C3, … |
| maximal normal subgroup of | (#857⋊C2)⋊D5, #4626⋊D5, C2×#66054⋊C3, … |
| maximal quotient of | #10606085⋊C3, #10606092⋊C3, #10606105⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6365);