Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ A4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×S4 |
| commutator, prime radical, cosocle | C2×C5×A4 | C22 |
| Fitting, socle | C23×C5 | C2×D3 |
| hypocenter | C5×A4 | Q8 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,3)(5,7,8,12)(6,9,10,11)(13,14,16,17,15);(2,3,4)(5,6,8,10)(7,11,12,9)(14,15)(16,17)Polycyclic presentation:
2^3,3,5,2^2|a^2=c,b^2=c,b^a=bc,e^a=e^4,d^b=d^2,f^b=g,g^b=f,f^d=g,g^d=fg34 conjugacy classes — view the full character table.
| maximal subgroup of | S4×Dic10, (C5⋊S4)⋊Q8, D5×A4⋊Q8, … |
| maximal normal subgroup of | S4×Dic10, (C5⋊S4)⋊Q8, D5×A4⋊Q8, … |
| maximal quotient of | #11751592, #11751595, #11751598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 975);