Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | Aut(G) = C2×C4×D3×AGL(1,𝔽5) (order 960) · Inn(G) = D3×AGL(1,𝔽5) · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ M32 |
| Sylow | C5 ⋊ #798 |
| Sylow | C3 ⋊ #3990 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×AGL(1,𝔽5) |
| commutator, socle | C2×C3×C5 | C2×C8 |
| Fitting | C3×C4×C5 | C2×C4 |
| prime radical | C2×D15 | C8 |
| cosocle | C3×#168 | C22 |
| hypocenter | C3×C5 | M32 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C4 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,5,4)(7,8)(9,11,13,20,14,12,19,21)(10,15,16,22,17,18,23,24);(2,3,4,5)(6,7,8)(9,10,12,15,13,16,21,22,14,17,11,18,19,23,20,24)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=d,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 | #11751642, D3×#3990, #11751644, … |
| maximal normal subgroup of | #11751642, D3×#3990, #11751644, … |
| maximal quotient of | #11746543, #11746547, #11746563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 242);