Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#4149 |
| Fitting | C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ H(5,𝔽2) |
| Sylow | C5 ⋊ C3×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C23×D5 |
| commutator, cosocle | C2×C5 | C24×C3 |
| Frattini | C2 | C23×C3×D5 |
| Fitting | C3×C5×#41 | C2 |
| socle | C2×C3×C5 | C24 |
| hypercenter | C3×#41 | D5 |
| hypocenter | C5 | C3×H(5,𝔽2) |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C3 ◁ C3×#41 | |
332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2,4,5,3)(6,12,9,8)(7,13,10,11)(14,15,16);(7,10)(11,13);(6,7)(8,11)(9,10)(12,13);(2,3)(4,5)(8,12)(11,13)111 conjugacy classes — view the full character table.
| maximal subgroup of | #11749415, #11749417, #11749418, … |
| maximal normal subgroup of | #11749415, #11749417, #11749418, … |
| maximal quotient of | C3×#65853, C3×#65855, C3×#65857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1146);