Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C8×D5 |
| Fitting | C2×C3×C5×C8 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C3×C8 |
| Hall | C3×C5 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C8 | D5 |
| commutator, hypocenter | C5 | C22×C3×C8 |
| Frattini | C4 | C22×C3×D5 |
| Fitting | C2×C3×C5×C8 | C2 |
| socle | C22×C3×C5 | C2×C4 |
| prime radical | C22×C3×D5 | C4 |
| cosocle | C4×C5 | C23×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C8 | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(3,4,5)(7,8)(9,10);(6,7,9,10,8)(11,12,13,15,14,16,17,18);(1,2)192 conjugacy classes — view the full character table.
| maximal subgroup of | #11745879, C3×#64727, C3×#64887, … |
| maximal normal subgroup of | #11745879, C3×#64727, C3×#64887, … |
| maximal quotient of | C3×C8×Dic10, C3×C4×C8×D5, C3×#64974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 692);