Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C26 |
| direct product | C137×#33522 |
| 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 | |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 173 points:
(1,2)(3,4)(5,6)(7,12)(8,11)(9,22)(10,15)(13,19)(14,20)(16,26)(17,23)(18,32)(21,25)(24,33)(27,31)(28,30)(29,34)(35,36)(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);(6,11)(8,19)(9,20)(12,23)(13,14)(15,25)(17,31)(18,30)(21,33)(22,24)(26,34)(27,28)(29,36)(32,35);(2,4)(5,7)(6,12)(8,17)(9,18)(10,16)(11,23)(13,27)(14,28)(15,26)(19,31)(20,30)(21,29)(22,32)(24,35)(25,34)(33,36);(7,16)(12,26)(17,29)(18,30)(23,34)(27,35)(28,32)(31,36)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26510);