Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #382 |
| Sylow | C5 ⋊ #4650 |
| Sylow | C3 ⋊ #64939 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D15 |
| commutator | C22×C3×C5 | C22×C4 |
| Fitting | C3×C5×#95 | C2 |
| socle, prime radical, cosocle | C23×C3×C5 | C23 |
| hypercenter | #95 | D15 |
| hypocenter | C3×C5 | #382 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ #95 | |
308 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=e,c^2=d,c^a=ce,g^a=g^2,h^a=h^4,c^b=cf168 conjugacy classes — view the full character table.
| maximal subgroup of | #14283344, #14283350, #14283366, … |
| maximal normal subgroup of | #14283344, #14283350, #14283366, … |
| maximal quotient of | #14279885, #14279888, #14279923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4946);