Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33853 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C4×D4×C137 ◁ C8×D4×C137 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 173 points:
(1,2)(3,4)(6,11)(7,16)(8,17)(9,18)(12,23)(13,19)(14,29)(15,27)(21,22)(24,34)(25,26)(28,33)(30,36)(32,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173);(5,6,10,14)(7,12,16,15)(8,19,21,35)(9,23,25,27)(11,26,29,18)(13,31,32,20)(17,28,22,36)(24,33,34,30);(2,4)(5,7,10,16)(6,12,14,15)(8,17,21,22)(9,18,25,26)(11,27,29,23)(13,30,32,33)(19,28,35,36)(20,34,31,24);(5,8,10,21)(6,13,14,32)(7,17,16,22)(9,24,25,34)(11,28,29,36)(12,30,15,33)(18,20,26,31)(19,27,35,23)7535 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26841);