Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of C5⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C5×SL(2,𝔽3) ⋊ C4 |
| Sylow | C5 ⋊ #859 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | C5⋊S4 |
| commutator, hypocenter | C5×SL(2,𝔽3) | C4 |
| Fitting | C2×C5×Q8 | D3 |
| socle | C22×C5 | S4 |
| prime radical, cosocle | C2×C5×SL(2,𝔽3) | C2 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4)(5,6,12,7,8,11,10,9)(14,15)(16,17);(6,9,12)(7,10,11)(13,14,16,17,15)Polycyclic presentation:
2^2,3,5,2^3|a^2=b,e^2=g,f^2=g,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^c=fg,f^c=ef,f^e=fg44 conjugacy classes — view the full character table.
| maximal subgroup of | #11751587, Dic5×#226, #11751590, … |
| maximal normal subgroup of | #11751587, Dic5×#226, #11751590, … |
| maximal quotient of | SL(2,𝔽3)⋊#168, C2×#91184, #13083943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 260);