Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D5×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C5×A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ C4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×S4 |
| commutator, hypocenter | C5×A4 | C2×C4 |
| Fitting, socle | C23×C5 | C2×D3 |
| prime radical | C2×C5⋊S4 | C2 |
| cosocle | C2×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2 | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,3,4,2)(5,6,8,7)(9,10,12,13,11);(1,2,4,3)(6,7,8)(10,11)(12,13)Polycyclic presentation:
2^3,3,5,2^2|a^2=c,b^2=c,e^a=e^4,d^b=d^2,f^b=g,g^b=f,f^d=g,g^d=fg40 conjugacy classes — view the full character table.
| maximal subgroup of | #11756708, #11756710, #11756747, … |
| maximal normal subgroup of | #11756708, #11756710, #11756747, … |
| maximal quotient of | #11751570, #11751572, #11751589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 977);