Finite Group DatabasebetaFinite Group Databasebeta| order | 19430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9715 |
| unambiguous semidirect product | C5⋊D1943 |
| unambiguous semidirect product | C29⋊D335 |
| unambiguous semidirect product | C67⋊D145 |
| Fitting, socle, derived, Hall | C5×C29×C67 ⋊ C2 |
| Hall | C29×C67 ⋊ D5 |
| Hall | C5×C67 ⋊ D29 |
| Hall | C5×C29 ⋊ D67 |
| Sylow | C67 ⋊ D145 |
| Sylow | C29 ⋊ D335 |
| Sylow | C5 ⋊ D1943 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C29×C67 | C2 |
| LCS | G ▷ C5×C29×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 9715 |
A minimal faithful permutation representation — 2 generators on 101 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(2,5)(3,4)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,101)(37,100)(38,99)(39,98)(40,97)(41,96)(42,95)(43,94)(44,93)(45,92)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)Polycyclic presentation:
2,5,29,67|b^a=b^4,c^a=c^28,d^a=d^664859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19430, 8);