Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C27 |
| direct product | C137×#23408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | #3449×C137 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
1946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 173 points:
(5,6,11,16)(7,17,19,29)(8,21,23,30)(9,15,10,14)(12,24,27,20)(13,25,28,22)(18,26,32,36)(31,33,35,34)(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);(1,2)(3,4)(5,7)(6,12)(8,18)(9,24)(10,20)(11,19)(13,26)(14,29)(15,17)(16,27)(21,35)(22,34)(23,32)(25,33)(28,36)(30,31);(2,4)(5,8)(6,13)(7,18)(9,22)(10,25)(11,23)(12,26)(14,21)(15,30)(16,28)(17,31)(19,32)(20,33)(24,34)(27,36)(29,35);(7,19)(12,27)(17,29)(18,32)(20,24)(26,36)(31,35)(33,34)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 16396);