Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4⋊C8 |
| Sylow | C5 ⋊ Dic3⋊C8 |
| Sylow | C3 ⋊ #4004 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×AGL(1,𝔽5) |
| commutator | C2×C3×C5 | C2×C8 |
| Fitting, socle, prime radical | C22×C3×C5 | C2×C4 |
| cosocle | C2×C3×Dic5 | C22 |
| hypocenter | C3×C5 | C4⋊C8 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,5,4)(7,8)(9,10,11,12)(13,15,17,16)(14,18,20,19);(2,3,4,5)(6,7,8)(10,12)(13,14,16,19,17,20,15,18)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=de,c^2=e,b^a=bd,g^a=g^2,f^b=f^2,g^c=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | #11751758, #11751759, #11751761, … |
| maximal normal subgroup of | #11751758, #11751759, #11751761, … |
| maximal quotient of | #11746513, #11746515, #11746563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 253);