Finite Group DatabasebetaFinite Group Databasebeta| order | 16422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D8211 |
| unambiguous semidirect product | C3⋊D2737 |
| unambiguous semidirect product | C7⋊D1173 |
| unambiguous semidirect product | C17⋊D483 |
| unambiguous semidirect product | C23⋊D357 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C17×C23 | C2 |
| LCS | G ▷ C3×C7×C17×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 8211 |
A minimal faithful permutation representation — 2 generators on 50 points:
(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(2,3)(5,10)(6,9)(7,8)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)Polycyclic presentation:
2,3,7,17,23|b^a=b^2,c^a=c^6,d^a=d^16,e^a=e^224107 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D357, D17×D483, D21×D391, … |
| maximal normal subgroup of | D23×D357, D17×D483, D21×D391, … |
| maximal quotient of | Dic8211, C2×D8211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16422, 17);