Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#5926 |
| Fitting | C5×2−1+4 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | C22×S4 |
| commutator, cosocle, hypocenter | SL(2,𝔽3) | C23×C5 |
| Frattini | C2 | C22×C5×S4 |
| Fitting | C5×2−1+4 | D3 |
| hypercenter | C5×D4 | S4 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C5×D4 | |
304 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
115 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#85469, C5×#85470, C5×#85473, … |
| maximal normal subgroup of | C5×#85469, C5×#85470, C5×#85473, … |
| maximal quotient of | C5×#85351, C5×#85353, C5×#85354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11084);