Finite Group DatabasebetaFinite Group Databasebeta| order | 440 |
| isoclinism | isoclinic class of D5 |
| automorphism | Aut(G) = C23×C5×AGL(1,𝔽5) (order 800) · Inn(G) = D5 · Out(G) = C24×C5 |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C4×D5×C11 |
| Fitting | C4×C5×C11 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C4×C11 |
| Hall | C5×C11 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C11 | D5 |
| commutator, hypocenter | C5 | C2×C4×C11 |
| Frattini | C2 | C2×D5×C11 |
| Fitting | C4×C5×C11 | C2 |
| socle | C2×C5×C11 | C22 |
| prime radical | C2×D5×C11 | C2 |
| cosocle | C2×C5 | C22×C11 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C4×C11 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 220 |
A minimal faithful permutation representation — 2 generators on 20 points:
(6,7)(8,9)(10,11,12,13,14,15,16,17,18,19,20);(1,2,3,4)(5,6,8,9,7)176 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C11⋊C8, #11724869, C8×D5×C11, … |
| maximal normal subgroup of | D5×C11⋊C8, #11724869, C8×D5×C11, … |
| maximal quotient of | C8×D5×C11, C11×#676, C4×C11×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(440, 30);