Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66084⋊C3 |
| Fitting | C5×#131 ⋊ C2×C3 |
| Hall | #66084 ⋊ C3 |
| Sylow | C5 ⋊ #568⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D5×A4 |
| commutator, hypocenter | C5×Q8 | C2×C3×C4 |
| Fitting | C5×#131 | C2×C3 |
| socle | C2×C5 | C2×C4×A4 |
| prime radical | D5×#41⋊C3 | C2 |
| cosocle | C5×#41 | C22×C3 |
| hypercenter | C8 | D5×A4 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C4 ◁ C8 | |
146 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 146 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) = 160 |
Polycyclic presentation:
2^2,3,2^3,5,2|b^2=d,d^2=h,e^2=h,f^2=h,b^a=bh,g^a=g^4,e^c=ef,f^c=e,f^e=fh94 conjugacy classes — view the full character table.
| maximal subgroup of | #14512941, #14512942, #14512945, … |
| maximal normal subgroup of | #14512941, #14512942, #14512945, … |
| maximal quotient of | #10611637⋊C3, #10611636⋊C3, SL(2,𝔽3)×#676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6372);