Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | A4×C22⋊D5 |
| unambiguous semidirect product | (C22×C22⋊D5)⋊C3 |
| Fitting | C24×C5 ⋊ C2×C3 |
| Hall | C22×C22⋊D5 ⋊ C3 |
| Sylow | C5 ⋊ D4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C22×C3 |
| Fitting | C24×C5 | C2×C3 |
| hypercenter | C22 | D5×A4 |
| hypocenter | C22×C5 | C3×D4 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ C22 | |
132 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,4,5,3)(7,8,9)(11,13);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13)52 conjugacy classes — view the full character table.
| maximal subgroup of | #11756793, #11756794, S4×C22⋊D5, … |
| maximal normal subgroup of | #11756793, #11756794, S4×C22⋊D5, … |
| maximal quotient of | A4×#683, A4×#685, A4×#686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1045);