Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C23×C4 |
| direct product | C137×#28766 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C22×D8×C137 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2,5,8)(3,7,4,6)(9,10,13,17)(11,20,22,15)(12,24,27,35)(14,19,26,18)(16,29,34,28)(21,37,39,33)(23,31,38,32)(25,30,40,36)(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);(1,3,5,4)(2,6,8,7)(9,11,14,23,13,22,26,38)(10,15,19,32,17,20,18,31)(12,25,29,39,27,40,28,21)(16,33,24,36,34,37,35,30);(1,3,5,4)(2,7,8,6)(9,12,26,29,13,27,14,28)(10,16,19,35,17,34,18,24)(11,21,38,25,22,39,23,40)(15,30,32,37,20,36,31,33);(1,4,5,3)(2,7,8,6)(10,17)(15,20)(16,34)(18,19)(24,35)(30,36)(31,32)(33,37)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 21754);