Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#13023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #447 |
| commutator | C2×C8 | C22×C4×C137 |
| Frattini, cosocle | C22×C8 | C23×C137 |
| prime radical | C2×#135×C137 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ #405×C137 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 3 generators on 173 points:
(2,4)(5,6,10,16,25,34,9,13,12,18,8,15,11,17,26,30)(7,19,22,14,28,29,27,36,24,35,20,33,23,31,21,32)(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)(6,13)(8,9)(10,26)(11,25)(14,29)(15,17)(16,34)(18,30)(19,36)(20,27)(21,22)(23,28)(31,33)(32,35);(5,7)(6,14)(8,21)(9,22)(10,27)(11,28)(12,24)(13,29)(15,19)(16,35)(17,36)(18,33)(20,26)(23,25)(30,31)(32,34)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 6011);