Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#121 ⋊ C2 |
| Hall | C3×C5 ⋊ #537 |
| Sylow | C5 ⋊ #5597 |
| Sylow | C3 ⋊ #65931 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×#121 | C2 |
| hypercenter | #121 | D15 |
| hypocenter | C3×C5 | #537 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #121 | |
588 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 588 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|a^2=f,d^a=df,g^a=g^2,h^a=h^4,c^b=cf,d^b=df,d^c=de120 conjugacy classes — view the full character table.
| maximal subgroup of | #14287818, #14287827, #14287835, … |
| maximal normal subgroup of | #14287818, #14287827, #14287835, … |
| maximal quotient of | #14322503, #14322842, #14323689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10551);