Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#91891 |
| Sylow | C5 ⋊ C2×#984 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C23 |
| Frattini | C2 | C2×D5×S4 |
| Fitting | C2×C5×Q8 | C2×D3 |
| socle | C22×C5 | C2×S4 |
| prime radical | C2×C5⋊(#41⋊C3) | C2 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
282 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #14512390, C4×#91891, #14512687, … |
| maximal normal subgroup of | #14512390, C4×#91891, #14512687, … |
| maximal quotient of | #14512637, #14512640, #14512649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10954);