Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #11752116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#127 ⋊ D3 |
| derived | C5×C42⋊C3 ⋊ C22 |
| Sylow | C5 ⋊ #857⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C42⋊C3 | C22 |
| Frattini | C22 | C2×C5⋊S4 |
| Fitting | C5×#127 | D3 |
| socle | C22×C5 | C2×S4 |
| LCS | G ▷ C5×C42⋊C3 | |
| UCS | C1 | |
166 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^2,3,5,2^4|e^2=g,f^2=gh,c^a=c^2,d^a=d^4,e^a=fh,f^a=eh,g^a=gh,e^b=eg,f^b=fgh,e^c=fg,f^c=ef,g^c=gh,h^c=g34 conjugacy classes — view the full character table.
| maximal subgroup of | #4626⋊D5, (#560⋊C3)⋊D5, D5×#857⋊C2, … |
| maximal normal subgroup of | #4626⋊D5, (#560⋊C3)⋊D5, D5×#857⋊C2, … |
| maximal quotient of | #14511906, #14511907, #14511908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6311);