Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×D3×#41 |
| Fitting | C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#41 |
| Sylow | C3 ⋊ C2×C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D3 |
| commutator, cosocle | C2×C3 | C24×C5 |
| Frattini | C2 | C23×C5×D3 |
| Fitting | C3×C5×#41 | C2 |
| socle | C2×C3×C5 | C24 |
| hypercenter | C5×#41 | D3 |
| hypocenter | C3 | C2×C5×#41 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,3,4,7)(2,6,5,8)(9,10,11)(12,13,14,15,16);(2,5)(6,8);(1,2)(3,6)(4,5)(7,8);(10,11)150 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3969, #11749429, C5×D3×#104, … |
| maximal normal subgroup of | D3×#3969, #11749429, C5×D3×#104, … |
| maximal quotient of | C5×#5517, C5×D3×#117, C5×#5522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1160);