Finite Group DatabasebetaFinite Group Databasebeta| order | 36701 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×7−1+2 |
| unambiguous semidirect product | C49⋊(C7×C107) |
| unambiguous semidirect product | (C49×C107)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C7×C107 | C72 |
| commutator, Frattini, cosocle | C7 | C72×C107 |
| prime radical | C72×C107 | C7 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C7×C107 ◁ G | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 156 |
| transitive degree | μt(G) = 5243 |
A minimal faithful permutation representation — 2 generators on 156 points:
(1,2,4,8,15,26,35,3,6,10,17,28,37,44,7,13,20,30,39,36,45,14,24,19,32,27,38,46,25,23,22,16,29,40,47,34,12,9,18,31,41,48,43,5,11,21,33,42,49)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156);(2,5,12,23,24,13,6)(4,9,19,10,11,22,20)(8,16,17,18,30,21,32)(15,27,33,39,31,28,29)(26,36,40,42,37,38,41)(35,44,45,46,47,48,49)5885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36701, 4);