Finite Group DatabasebetaFinite Group Databasebeta| order | 36693 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C151 · Schur multiplier (H2) = C9 |
| direct product | C151×#6898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C151 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C151 |
| prime radical | C33×C151 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C151 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 205 |
| transitive degree | μt(G) = 12231 |
A minimal faithful permutation representation — 3 generators on 205 points:
(1,2,5)(3,7,13)(4,8,12)(6,14,11)(9,16,21)(10,17,20)(15,22,19)(18,24,26)(23,27,25)(28,29,32)(30,33,39)(31,35,40)(34,44,38)(36,41,47)(37,43,48)(42,51,46)(45,50,53)(49,54,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205);(2,6,8)(5,12,14)(7,15,17)(13,20,22)(16,23,24)(21,26,27)(28,30,36,31,37,45,38,46,52)(29,33,41,35,43,50,34,42,49)(32,39,47,40,48,53,44,51,54);(1,3,9,11,19,25,4,10,18)(2,7,16,6,15,23,8,17,24)(5,13,21,14,22,27,12,20,26)(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54)7701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36693, 45);