Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Hall | C3×C5 ⋊ C4×C8 |
| Sylow | C5 ⋊ C8×Dic3 |
| Sylow | C3 ⋊ C8×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D3×D5 |
| commutator, hypocenter | C3×C5 | C4×C8 |
| Fitting, cosocle | C2×C3×C4×C5 | C22 |
| socle, prime radical | C22×C3×C5 | C2×C4 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,5,3)(7,8)(13,15,20,19,17,18,16,14);(2,3)(4,5)(6,7,8)(9,10,11,12)(13,14,16,18,17,19,20,15)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=cd,c^2=e,g^a=g^4,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | #11746541, #11746543, #11746563, … |
| maximal normal subgroup of | #11746541, #11746543, #11746563, … |
| maximal quotient of | C3⋊C8×#168, #11745833, #11745872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 27);