Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33611 |
| 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 ◁ C2×#41×C137 ◁ C2×#131×C137 ◁ G | |
674 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)(5,6)(7,16)(8,13)(9,23)(10,22)(11,15)(12,19)(14,24)(17,29)(18,30)(20,36)(21,32)(25,26)(27,33)(28,35)(31,34)(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);(5,7,17,33,10,20,9,19,11,21,24,34,8,18,25,35)(6,12,26,36,13,27,14,16,15,28,23,30,22,31,29,32);(2,4)(5,6)(7,12)(8,22)(9,14)(10,13)(11,15)(16,19)(17,26)(18,31)(20,27)(21,28)(23,24)(25,29)(30,34)(32,35)(33,36);(5,8,11,10)(6,13,15,22)(7,18,21,20)(9,17,25,24)(12,27,28,31)(14,23,29,26)(16,30,32,36)(19,33,35,34)7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26599);