Finite Group DatabasebetaFinite Group Databasebeta| order | 35970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17985 |
| unambiguous semidirect product | C3⋊D5995 |
| unambiguous semidirect product | C5⋊D3597 |
| unambiguous semidirect product | C11⋊D1635 |
| unambiguous semidirect product | C109⋊D165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C11×C109 | C2 |
| LCS | G ▷ C3×C5×C11×C109 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 128 |
| transitive degree | μt(G) = 17985 |
A minimal faithful permutation representation — 2 generators on 128 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128);(2,3)(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,128)(22,127)(23,126)(24,125)(25,124)(26,123)(27,122)(28,121)(29,120)(30,119)(31,118)(32,117)(33,116)(34,115)(35,114)(36,113)(37,112)(38,111)(39,110)(40,109)(41,108)(42,107)(43,106)(44,105)(45,104)(46,103)(47,102)(48,101)(49,100)(50,99)(51,98)(52,97)(53,96)(54,95)(55,94)(56,93)(57,92)(58,91)(59,90)(60,89)(61,88)(62,87)(63,86)(64,85)(65,84)(66,83)(67,82)(68,81)(69,80)(70,79)(71,78)(72,77)(73,76)(74,75)Polycyclic presentation:
2,3,5,11,109|b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^1088994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35970, 19);