Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#4044 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #126 |
| Sylow | C5 ⋊ C3×#126 |
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(7,11)(10,13)(14,20,17,16)(15,21,18,19)(22,23,24);(6,12,9,8)(7,13,11,10)(15,18)(16,20);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,19)(17,18)(20,21)102 conjugacy classes — view the full character table.
| maximal subgroup of | #11753558, #11753559, #11753561, … |
| maximal normal subgroup of | #11753558, #11753559, #11753561, … |
| maximal quotient of | C3×#64940, C3×#64943, C3×#64949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 691);