Finite Group DatabasebetaFinite Group Databasebeta| order | 29190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#19154254 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C139 | C2×C3 |
| LCS | G ▷ C5×C7×C139 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 4865 |
A minimal faithful permutation representation — 2 generators on 151 points:
(2,3)(4,5)(7,10,11,8,9,12)(14,18,19,15,16,20)(17,26,27,21,22,36)(23,39,40,29,30,53)(24,38,34,32,28,25)(31,58,59,42,43,76)(33,56,57,45,41,50)(35,37,55,47,48,51)(44,81,82,61,62,105)(46,79,80,64,60,73)(49,54,78,66,67,74)(52,94,92,70,71,69)(63,110,111,84,85,135)(65,108,109,87,83,102)(68,77,107,89,90,103)(72,122,114,95,96,98)(75,126,120,99,100,93)(86,127,128,113,101,145)(88,137,138,115,112,133)(91,106,136,117,118,134)(97,141,140,123,124,130)(104,148,119,131,132,121)(116,146,147,139,129,150)(125,151,144,142,143,149);(1,2,4,5,3)(6,7,9,12,11,10,8)(13,14,17,23,31,44,63,86,114,80,40,55,56,39,54,75,101,129,143,147,111,136,148,145,141,137,110,131,90,43,60,71,74,76,102,130,139,115,87,64,45,32,16,20,25,35,49,68,91,119,120,92,57,27,38,26,37,52,72,97,125,144,138,82,107,126,122,108,81,106,118,62,83,96,100,103,105,133,149,142,123,95,70,48,22,28,36,50,69,93,121,117,89,66,47,34,19,18,24,33,46,65,88,116,140,109,59,78,94,79,58,77,104,85,112,124,128,132,134,135,150,151,146,127,99,67,30,41,51,53,73,98,113,84,61,42,29,21,15)Polycyclic presentation:
2,3,5,7,139|c^a=c^4,d^a=d^6,e^a=e^138,d^b=d^2,e^b=e^42822 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29190, 48);