Finite Group DatabasebetaFinite Group Databasebeta| order | 33330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013203 |
| 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)(5,9,10,8,13,6,7,14,11,12)(16,20,21,39,43,17,18,26,28,65)(19,33,34,88,35,23,24,54,55,57)(22,48,49,50,71,30,31,77,78,80)(25,59,60,40,99,36,37,94,66,67)(27,68,69,95,47,41,42,100,61,76)(29,73,74,64,72,45,46,75,44,79)(32,82,83,110,58,51,52,87,93,92)(38,97,89,90,106,62,63,56,112,84)(53,108,98,104,113,85,86,107,91,111)(70,114,109,81,115,102,103,96,105,101);(1,2,3)(4,5,8,13,7,10,14,9,12,11,6)(15,16,19,25,38,64,39,37,61,96,108,100,88,80,65,76,45,26,40,31,50,81,72,77,90,103,110,92,57,33,46,75,104,89,54,41,18,22,32,53,87,111,67,63,98,106,82,102,68,101,60,94,115,42,70,52,84,107,97,99,113,83,85,51,30,20,27,34,56,91,74,73,24,35,58,93,114,112,49,79,105,78,48,66,21,29,47,43,71,55,69,86,109,95,59,28,44,62,36,23,17)Polycyclic presentation:
2,3,5,11,101|b^a=b^2,d^a=d^10,e^a=e^100,d^c=d^4,e^c=e^36348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33330, 62);