Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D4×A4 |
| unambiguous semidirect product | C4⋊(C2×C5×A4) |
| unambiguous semidirect product | (C22×D4)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×D4)⋊C3 |
| Fitting, Hall | C22×C5×D4 ⋊ C3 |
| Sylow | C22×D4 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C22×A4 |
| commutator, cosocle | C23 | C22×C3×C5 |
| Frattini | C2 | C22×C5×A4 |
| Fitting | C22×C5×D4 | C3 |
| socle | C23×C5 | C22×C3 |
| hypercenter | C5×D4 | A4 |
| hypocenter | C22 | C3×C5×D4 |
| LCS | G ▷ C23 ▷ C22 | |
| UCS | C1 ◁ C2×C5 ◁ C5×D4 | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 13 points:
(2,3,4)(6,8)(9,10,11,12,13);(1,4)(2,3)(5,6)(7,8)100 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#5414, C5×#5415, #11752133, … |
| maximal normal subgroup of | C5×#5414, C5×#5415, #11752133, … |
| maximal quotient of | C5×A4×C22⋊C4, C5×A4×C4⋊C4, C5×#548⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1127);