Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | D5×#131⋊C3 |
| unambiguous semidirect product | (D5×#131)⋊C3 |
| Fitting | C5×#131 ⋊ C2×C3 |
| Hall | D5×#131 ⋊ C3 |
| Sylow | C5 ⋊ C2×#131⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×A4 |
| commutator, hypocenter | C5×Q8 | C2×C3×C4 |
| Frattini | C4 | C2×D5×A4 |
| Fitting | C5×#131 | C2×C3 |
| socle | C2×C5 | C2×C4×A4 |
| prime radical | D5×#41⋊C3 | C2 |
| cosocle | C5×#41 | C22×C3 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C8 | |
152 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4628, #14511743, D5×#504⋊C3, … |
| maximal normal subgroup of | D5×#4628, #14511743, D5×#504⋊C3, … |
| maximal quotient of | C8×C5⋊(#41⋊C3), #10611638⋊C3, C8×D5×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6371);