Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ #131 |
| Sylow | C5 ⋊ #907 |
| Sylow | C3 ⋊ #4053 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D15 |
| commutator, socle | C2×C3×C5 | C22×C4 |
| Fitting | C3×C5×M16 | C2 |
| prime radical | #6817 | C2 |
| cosocle | C3×C4×C5 | C23 |
| hypercenter | M16 | D15 |
| hypocenter | C3×C5 | #131 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 ◁ M16 | |
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)(9,11,12,18,13,17,19,23)(10,15,16,22,14,20,21,24);(10,14)(11,17)(16,21)(18,23);(2,3)(4,5)(7,8)(9,10)(11,15)(12,16)(13,14)(17,20)(18,22)(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^4,c^b=ce90 conjugacy classes — view the full character table.
| maximal subgroup of | #11748174, #11748175, #11748176, … |
| maximal normal subgroup of | #11748174, #11748175, #11748176, … |
| maximal quotient of | #11750802, #11750807, #11750809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 872);