Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66168⋊C3 |
| Hall | #66168 ⋊ C3 |
| Sylow | C5 ⋊ C4⋊(#41⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×A4 |
| commutator, cosocle | C2×C5×Q8 | C22×C3 |
| Fitting | C2×C5×#41 | C2×C3 |
| socle | C22×C5 | C22×A4 |
| hypercenter | C2×C4 | D5×A4 |
| hypocenter | C5×Q8 | C3×D4 |
| LCS | G ▷ C2×C5×Q8 ▷ C5×Q8 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
174 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^2,3,2^3,5,2|a^2=d,b^2=h,e^2=h,f^2=h,b^a=bd,g^a=g^4,e^c=f,f^c=efh,f^e=fh91 conjugacy classes — view the full character table.
| maximal subgroup of | #14513403, #14513405, #14513406, … |
| maximal normal subgroup of | #14513403, #14513405, #14513406, … |
| maximal quotient of | SL(2,𝔽3)×#683, #10614188⋊C3, #10615313⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6393);