Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×GL(2,𝔽3) |
| Fitting | C5×Q8 ⋊ C4×D3 |
| derived | C5×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C5 ⋊ C4×GL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C2×C4 |
| Fitting | C5×Q8 | C4×D3 |
| socle | C2×C5 | C4×S4 |
| prime radical | D5×GL(2,𝔽3) | C2 |
| cosocle | D5×SL(2,𝔽3) | C22 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
176 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10901);