Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×Q8 |
| Sylow | C5 ⋊ C4×Dic6 |
| Sylow | C3 ⋊ #4033 |
140 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,11,12,10)(15,19)(17,20);(7,8)(13,15,16,19)(14,17,18,20);(2,3)(4,5)(9,10,12,11)(13,14,16,18)(15,17,19,20)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=d,c^2=de,g^a=g^4,c^b=cd,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | #11751758, #11751761, #11751765, … |
| maximal normal subgroup of | #11751758, #11751761, #11751765, … |
| maximal quotient of | #11747564, #11747568, #11747820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 399);