Finite Group DatabasebetaFinite Group Databasebeta| order | 440 |
| isoclinism | isoclinic class of D4×C11⋊C5 |
| automorphism | Aut(G) = D4×AGL(1,𝔽11) (order 880) · Inn(G) = C22×C11⋊C5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D4×C11⋊C5 |
| unambiguous semidirect product | C4⋊(C2×C11⋊C5) |
| unambiguous semidirect product | C22⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (D4×C11)⋊C5 |
| Fitting, Hall | D4×C11 ⋊ C5 |
| Sylow | C11 ⋊ C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C11⋊C5 |
| commutator, socle, cosocle | C2×C11 | C22×C5 |
| Fitting | D4×C11 | C5 |
| hypercenter | D4 | C11⋊C5 |
| hypocenter | C11 | C5×D4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 44 |
A minimal faithful permutation representation — 2 generators on 15 points:
(2,3,5,8,7)(4,6,10,11,9)(13,15);(1,2,4,7,3,5,9,11,6,8,10)(12,13)(14,15)35 conjugacy classes — view the full character table.
| maximal subgroup of | #4323⋊C5, #4324⋊C5, D8×C11⋊C5, … |
| maximal normal subgroup of | #4323⋊C5, #4324⋊C5, D8×C11⋊C5, … |
| maximal quotient of | C22⋊C4×C11⋊C5, C4⋊C4×C11⋊C5, D8×C11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(440, 13);