Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6773 |
| Hall | C3×C5 ⋊ C2×#41 |
| Sylow | C5 ⋊ C2×#235 |
| Sylow | C3 ⋊ C2×#713 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×D5 |
| commutator, cosocle | C2×C3×C5 | C24 |
| Frattini | C2 | C22×D3×D5 |
| Fitting | C2×C3×C4×C5 | C22 |
| socle | C22×C3×C5 | C23 |
| hypercenter | C2×C4 | D3×D5 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 18 points:
(3,4,5)(6,7,9,10,8)(11,13,14,18)(12,16,15,17);(1,2)(4,5)(11,12,14,15)(13,17,18,16);(7,8)(9,10)(12,15)(16,17);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #11747500, #11747501, #11747512, … |
| maximal normal subgroup of | #11747500, #11747501, #11747512, … |
| maximal quotient of | #11752464, #11752468, #11752486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1085);