Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#18844 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | #3515×C137 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 177 points:
(2,5)(3,7)(6,8)(9,10,15,20)(11,16,23,31)(12,24,26,34)(13,19,14,18)(17,28,32,25)(21,35,37,39)(22,33,27,30)(29,36,40,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(1,2,4,6)(3,8,7,5)(9,11)(10,16)(12,21)(13,22)(14,27)(15,23)(17,29)(18,30)(19,33)(20,31)(24,39)(25,36)(26,37)(28,38)(32,40)(34,35);(9,12)(10,17)(11,21)(13,25)(14,28)(15,26)(16,29)(18,24)(19,34)(20,32)(22,36)(23,37)(27,38)(30,39)(31,40)(33,35);(2,6)(5,8)(9,13,15,14)(10,18,20,19)(11,22,23,27)(12,25,26,28)(16,30,31,33)(17,24,32,34)(21,36,37,38)(29,39,40,35)5069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 11832);