Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C3⋊#170 |
| derived, Hall | C3×C5 ⋊ C23×C8 |
| Sylow | C5 ⋊ C23×C3⋊C8 |
| Sylow | C3 ⋊ C23×#170 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C23×C8 |
| Frattini | C2 | C23×ΓL(1,𝔽16) |
| Fitting, socle, prime radical | C24×C3×C5 | C4 |
| cosocle | C3×Dic5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C24 | |
676 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11746789, C2×#11746570, #14294345, … |
| maximal normal subgroup of | C2×#11746789, C2×#11746570, #14294345, … |
| maximal quotient of | C22×C4×C3⋊#170, C22×#91241, C22×C4⋊(C3⋊#170), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11191);