Finite Group DatabasebetaFinite Group Databasebeta| order | 33150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16575 |
| unambiguous semidirect product | C3⋊D5525 |
| unambiguous semidirect product | C13⋊D1275 |
| unambiguous semidirect product | C17⋊D975 |
| unambiguous semidirect product | C25⋊D663 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C13×C17×C25 | C2 |
| Frattini | C5 | D3315 |
| socle | C3×C5×C13×C17 | D5 |
| LCS | G ▷ C3×C13×C17×C25 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 16575 |
A minimal faithful permutation representation — 2 generators on 58 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);(2,3)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)Polycyclic presentation:
2,3,5,13,17,5|c^5=f^4,b^a=b^2,c^a=c^4f,d^a=d^12,e^a=e^16,f^a=f^48289 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33150, 17);