Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90937 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q32 |
| Sylow | C5 ⋊ #829 |
| Sylow | C3 ⋊ #3961 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6652 |
| commutator, Fitting, cosocle | C3×C5×C8 | C22 |
| Frattini, hypercenter | C8 | D3×D5 |
| socle, prime radical | C2×C3×C5 | D8 |
| hypocenter | C3×C5 | Q32 |
| LCS | G ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,4,5,3)(7,8)(9,11,14,22)(10,15,18,32)(12,24,27,40)(13,29,25,21)(16,34,35,39)(17,36,28,31)(19,37,38,23)(20,33,30,26);(2,3)(4,5)(6,7,8)(9,10,14,18)(11,19,22,38)(12,23,27,37)(13,28,25,17)(15,30,32,20)(16,33,35,26)(21,39,29,34)(24,36,40,31)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11746831, #11746840, #11746841, … |
| maximal normal subgroup of | #11746831, #11746840, #11746841, … |
| maximal quotient of | #11745897, #11745899, #11745940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 22);