Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C5×C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #131 |
| Sylow | C5 ⋊ #901 |
| Sylow | C3 ⋊ #4047 |
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)(9,11,12,17,13,18,19,23)(10,15,16,22,14,20,21,24);(10,14)(15,20)(16,21)(22,24);(2,3)(4,5)(7,8)(9,10)(11,15)(12,16)(13,14)(17,22)(18,20)(19,21)(23,24)Polycyclic presentation:
2^5,3,5|c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^4132 conjugacy classes — view the full character table.
| maximal subgroup of | #11745889, #11745890, #11746329, … |
| maximal normal subgroup of | #11745889, #11745890, #11746329, … |
| maximal quotient of | C8×Dic30, #11750780, C8×D60, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 866);