Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×M32 ⋊ C2 |
| Hall | C3×C5 ⋊ #504 |
| Sylow | C5 ⋊ #4907 |
| Sylow | C3 ⋊ #65196 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D15 |
| commutator, socle | C2×C3×C5 | C22×C8 |
| Fitting | C3×C5×M32 | C2 |
| prime radical | #6817 | C4 |
| cosocle | C3×C5×C8 | C23 |
| hypercenter | M32 | D15 |
| hypocenter | C3×C5 | #504 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C8 ◁ M32 | |
168 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^2,h^a=h^4,c^b=cf180 conjugacy classes — view the full character table.
| maximal subgroup of | #14315182, #14315188, #14315202, … |
| maximal normal subgroup of | #14315182, #14315188, #14315202, … |
| maximal quotient of | #14312639, #14312642, #14312853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5203);