Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6706 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #904 |
| Sylow | C3 ⋊ #4050 |
124 conjugacy classes of subgroups.
| 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)(6,7,8)(9,12,13,20,14,21,11,18)(10,16,15,19,17,23,22,24);(9,11,14,13)(10,15,17,22)(12,18,21,20)(16,19,23,24);(2,3)(4,5)(7,8)(9,10)(11,15)(12,19)(13,22)(14,17)(16,20)(18,23)(21,24)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #11745907, #11745908, #11745913, … |
| maximal normal subgroup of | #11745907, #11745908, #11745913, … |
| maximal quotient of | #11750784, C4×#6706, C4×D120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 869);