Finite Group DatabasebetaFinite Group Databasebeta| order | 33150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C17⋊#14519615 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C17 | C2×C3 |
| LCS | G ▷ C52×C13×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3315 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,4)(3,13,9,6,7,15)(5,10,14,11,12,8)(17,21,22,18,19,23)(20,27,26,24,25,28)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45);(1,3,8,14,6)(2,5,7,13,11)(4,9,10,12,15)(16,17,20,19,23,26,25,27,28,22,21,24,18)(29,30,32,34,36,38,40,42,44,45,43,41,39,37,35,33,31)Polycyclic presentation:
2,3,5^2,13,17|c^a=c^4,d^a=d^4,e^a=e^12,f^a=f^16,c^b=cd,d^b=c^2d^3,e^b=e^3948 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33150, 39);