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 ⋊ Q8×Dic3 |
| Sylow | C3 ⋊ #4033 |
140 conjugacy classes of subgroups.
| 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)(13,15,16,20)(14,17,18,19);(7,8)(9,10,11,12)(15,20)(17,19);(2,3)(4,5)(13,14,16,18)(15,19,20,17)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=d,c^2=e,c^a=ce,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11747271, #11747272, #11747273, … |
| maximal normal subgroup of | #11747271, #11747272, #11747273, … |
| maximal quotient of | #11746846, #11746848, #11746862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 407);