Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #97 |
| Sylow | C5 ⋊ #815 |
| Sylow | C3 ⋊ #3992 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×AGL(1,𝔽5) |
| commutator, socle | C2×C3×C5 | C42 |
| Fitting | C3×C4×C5 | C2×C4 |
| prime radical | C2×C3×D5 | C2×C4 |
| cosocle | C3×C4×D5 | C22 |
| hypocenter | C3×C5 | #97 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,3,5,4)(7,8)(9,11,12,14,13,15,16,10);(2,3,4,5)(6,7,8)(9,10,12,11,13,14,16,15)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=e,d^2=e,b^a=be,g^a=g^2,f^b=f^2,g^c=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×ΓL(1,𝔽25), D3×#3992, #11751655, … |
| maximal normal subgroup of | AGL(1,𝔽5)×ΓL(1,𝔽25), D3×#3992, #11751655, … |
| maximal quotient of | #11746454, #11746455, #11746485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 226);