Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×#672 |
| derived, Sylow | C5 ⋊ C22×C3×C16 |
| Hall | C3×C5 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C8 | D5 |
| commutator, hypocenter | C5 | C22×C3×C16 |
| Frattini | C8 | C22×C3×D5 |
| Fitting | C22×C3×C5×C8 | C2 |
| socle, prime radical | C23×C3×C5 | C8 |
| cosocle | C5×C8 | C23×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C3×C8 | |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598295, C3×#10598148, #14278691, … |
| maximal normal subgroup of | C3×#10598295, C3×#10598148, #14278691, … |
| maximal quotient of | C2×C3×C4×#672, C2×C3×C22⋊#672, C2×C3×C4⋊#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4188);