Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C22⋊C8 |
| Sylow | C5 ⋊ (C2×D3)⋊C8 |
| Sylow | C3 ⋊ #4003 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,5,4)(7,8)(10,12)(13,15,17,16)(14,18,20,19);(2,3,4,5)(6,7,8)(9,10)(11,12)(13,14,16,19,17,20,15,18)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,c^2=e,b^a=bd,g^a=g^2,f^b=f^2,g^c=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | #11751760, #11751763, #11751764, … |
| maximal normal subgroup of | #11751760, #11751763, #11751764, … |
| maximal quotient of | #11746490, #11746491, #11746494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 247);