Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #95 |
| Sylow | C5 ⋊ C3⋊#95 |
| Sylow | C3 ⋊ #3963 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D3×D5 |
| commutator | C2×C3×C5 | C42 |
| Fitting, socle, prime radical, cosocle | C23×C3×C5 | C22 |
| hypocenter | C3×C5 | #95 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 | |
152 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,5,3)(7,8)(13,14,15,16)(18,20);(2,3)(4,5)(6,7,8)(9,10,11,12)(17,18)(19,20)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,b^a=be,g^a=g^4,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11748567, #11748568, #11748569, … |
| maximal normal subgroup of | #11748567, #11748568, #11748569, … |
| maximal quotient of | #11745966, #11745967, #11745968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 70);