Finite Group DatabasebetaFinite Group Databasebeta| order | 440 |
| isoclinism | isoclinic class of #89167 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C11 ⋊ D4 |
| Sylow | C11 ⋊ D20 |
| Sylow | C5 ⋊ C22⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D11 |
| commutator, Fitting, socle, cosocle | C2×C5×C11 | C22 |
| hypocenter | C5×C11 | D4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 | |
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:
(1,2,4,6,8,10,11,9,7,5,3)(13,14)(15,16)(18,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,15,16,14)(17,18,19,20)Polycyclic presentation:
2^3,5,11|a^2=c,b^a=bc,e^a=e^10,d^b=d^453 conjugacy classes — view the full character table.
| maximal subgroup of | #11724985, #11724986, #11724988, … |
| maximal normal subgroup of | #11724985, #11724986, #11724988, … |
| maximal quotient of | #11724873, #11724878, #11724879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(440, 22);