Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #983 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C22 |
| Fitting | C5×Q8 | C2×D3 |
| socle | C2×C5 | C2×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,3,12,4,5,11,10,9)(2,13,16,14,6,7,15,8)(17,18,20,21,19);(1,2)(3,14,12,7,9,16)(4,15,11,8,10,13)(5,6)(18,19)(20,21)Polycyclic presentation:
2^2,3,5,2^3|e^2=g,f^2=g,b^a=bg,d^a=d^4,c^b=c^2,e^b=f,f^b=e,e^c=fg,f^c=ef,f^e=fg29 conjugacy classes — view the full character table.
| maximal subgroup of | #11756766, C2×#91896, D5×#983, … |
| maximal normal subgroup of | #11756766, C2×#91896, D5×#983, … |
| maximal quotient of | #11751591, #11751592, #11751600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 972);