Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #400 |
| Sylow | C5 ⋊ #4659 |
| Sylow | C3 ⋊ #64949 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D3×D5 |
| commutator, socle, prime radical, cosocle | C23×C3×C5 | C23 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #400 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
268 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 96 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=e,b^2=ef,c^2=d,b^a=bd,c^a=cef,h^a=h^4,c^b=cf,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64949, #14332050, C2×#11748583, … |
| maximal normal subgroup of | D3×#64949, #14332050, C2×#11748583, … |
| maximal quotient of | #14280154, #14280182, #14280185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2778);