Finite Group DatabasebetaFinite Group Databasebeta| order | 440 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | Aut(G) = D4×AGL(1,𝔽11) (order 880) · Inn(G) = AGL(1,𝔽11) · Out(G) = D4 |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic11⋊C5 |
| unambiguous semidirect product | (C2×Dic11)⋊C5 |
| unambiguous semidirect product | (C2×C11⋊C5)⋊C4 |
| derived, Sylow | C11 ⋊ C2×C4×C5 |
| Hall | C2×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C2×C4×C5 |
| Frattini | C2 | C2×AGL(1,𝔽11) |
| Fitting, socle | C22×C11 | C2×C5 |
| prime radical | C22×C11⋊C5 | C2 |
| cosocle | C2×C11 | C22×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 88 |
A minimal faithful permutation representation — 2 generators on 17 points:
(3,4,5,6)(8,11,12,16,15,9,10,13,14,17);(1,2)(7,8,11,14,12,15,17,13,16,10,9)44 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic11⋊C5, (Dic11⋊C4)⋊C5, C4⋊(Dic11⋊C5), … |
| maximal normal subgroup of | C4×Dic11⋊C5, (Dic11⋊C4)⋊C5, C4⋊(Dic11⋊C5), … |
| maximal quotient of | C2×(C11⋊C5)⋊C8, #4318⋊C5, C4×Dic11⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(440, 10);