Finite Group DatabasebetaFinite Group Databasebeta| order | 33330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C101⋊C5)⋊D11) |
| unambiguous semidirect product | (C101⋊C5)⋊D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C101 | C2×C5 |
| LCS | G ▷ C3×C11×C101 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 3333 |
A minimal faithful permutation representation — 2 generators on 115 points:
(2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(16,20,21,39,44,17,18,26,28,60)(19,33,34,85,63,23,24,53,55,91)(22,49,50,51,70,30,31,78,79,81)(25,58,27,64,65,36,37,41,42,93)(29,72,73,54,71,46,47,74,45,80)(32,59,83,112,92,38,52,89,109,108)(35,62,43,97,90,56,40,67,68,61)(48,101,102,111,96,75,76,115,86,106)(57,94,95,104,105,87,66,113,77,82)(69,98,100,84,114,88,99,107,103,110);(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(15,16,19,25,38,30,20,27,43,69,87,56,33,54,39,61,81,60,58,73,72,100,50,80,52,84,101,111,85,53,31,51,82,108,91,62,21,29,48,77,106,94,64,89,95,112,115,99,97,114,65,93,110,68,98,102,109,113,83,42,66,96,104,75,46,26,40,63,92,105,79,49,34,55,86,76,103,59,71,78,107,47,74,37,44,70,90,28,45,24,35,57,88,67,41,18,22,32,36,23,17)Polycyclic presentation:
2,3,5,11,101|b^a=b^2,d^a=d^10,e^a=e^100,e^c=e^95420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33330, 59);