Finite Group DatabasebetaFinite Group Databasebeta| order | 20370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10185 |
| unambiguous semidirect product | C3⋊D3395 |
| unambiguous semidirect product | C5⋊D2037 |
| unambiguous semidirect product | C7⋊D1455 |
| unambiguous semidirect product | C97⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C97 | C2 |
| LCS | G ▷ C3×C5×C7×C97 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 112 |
| transitive degree | μt(G) = 10185 |
A minimal faithful permutation representation — 2 generators on 112 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112);(2,3)(5,8)(6,7)(10,15)(11,14)(12,13)(17,112)(18,111)(19,110)(20,109)(21,108)(22,107)(23,106)(24,105)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)Polycyclic presentation:
2,3,5,7,97|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^965094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D30555 |
| maximal quotient of | D30555 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20370, 20);