Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×C4⋊Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ #536 |
| Sylow | C5 ⋊ #5724 |
| Sylow | C3 ⋊ #66058 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×C4⋊Q8 | C2 |
| prime radical | C2×#6821 | C2 |
| hypercenter | C4⋊Q8 | D15 |
| hypocenter | C3×C5 | #536 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
540 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 147 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|b^2=e,c^2=e,d^2=f,d^a=de,g^a=g^2,h^a=h^4,c^b=ce,d^c=df120 conjugacy classes — view the full character table.
| maximal subgroup of | #14313675, #14313700, #14313747, … |
| maximal normal subgroup of | #14313675, #14313700, #14313747, … |
| maximal quotient of | #14322465, #14322515, #14322883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10678);