Finite Group DatabasebetaFinite Group Databasebeta| order | 37050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13×C19 | C2×C3 |
| LCS | G ▷ C52×C13×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 3705 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,4)(3,13,9,7,6,10)(5,15,14,11,12,8)(17,21,22,18,19,23)(20,27,26,24,25,28)(30,34,35,31,32,36)(33,42,39,37,38,44)(40,45,47,46,43,41);(1,3,8,14,7)(2,5,6,13,11)(4,9,15,12,10)(16,17,20,19,23,26,25,27,28,22,21,24,18)(29,30,33,39,45,42,46,32,36,41,47,35,34,40,38,43,44,37,31)Polycyclic presentation:
2,3,5^2,13,19|c^a=c^4,d^a=d^4,e^a=e^12,f^a=f^18,c^b=cd^3,d^b=c^4d^3,e^b=e^3,f^b=f^71035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37050, 74);