Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #557 |
| Sylow | C5 ⋊ #5567 |
| Sylow | C3 ⋊ #65901 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C4×C5×Q8 | C2 |
| hypercenter | C4×Q8 | D15 |
| hypocenter | C3×C5 | #557 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
400 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 155 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=f,c^2=e,d^2=ef,b^a=bf,g^a=g^2,h^a=h^4,d^c=de165 conjugacy classes — view the full character table.
| maximal subgroup of | #14289153, #14289165, #14289182, … |
| maximal normal subgroup of | #14289153, #14289165, #14289182, … |
| maximal quotient of | C4⋊C4×Dic30, #14327274, #14327773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10521);