Finite Group DatabasebetaFinite Group Databasebeta| order | 21210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10605 |
| unambiguous semidirect product | C3⋊D3535 |
| unambiguous semidirect product | C5⋊D2121 |
| unambiguous semidirect product | C7⋊D1515 |
| unambiguous semidirect product | C101⋊D105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C101 | C2 |
| LCS | G ▷ C3×C5×C7×C101 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 116 |
| transitive degree | μt(G) = 10605 |
A minimal faithful permutation representation — 2 generators on 116 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116);(2,3)(5,8)(6,7)(10,15)(11,14)(12,13)(17,116)(18,115)(19,114)(20,113)(21,112)(22,111)(23,110)(24,109)(25,108)(26,107)(27,106)(28,105)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,98)(36,97)(37,96)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)Polycyclic presentation:
2,3,5,7,101|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^1005304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31815 |
| maximal quotient of | D31815 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21210, 19);