Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C137 · Schur multiplier (H2) = C25×C4 |
| direct product | C137×#20399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C22×C22⋊C4 |
| commutator | C22 | C22×C42×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C24×C137 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×#117×C137 ◁ G | |
1442 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 173 points:
(1,2,4,3)(5,6)(7,16)(8,13)(9,14)(10,24)(11,15)(12,19)(17,30)(18,31)(20,26)(21,27)(22,29)(23,28)(25,33)(32,36)(34,35)(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);(5,7,10,20,11,19,9,18)(6,12,14,26,15,16,24,31)(8,17,21,32,22,33,23,34)(13,25,28,36,29,30,27,35);(1,3,4,2)(5,8,11,22)(6,13,15,29)(7,17,19,33)(9,23,10,21)(12,25,16,30)(14,28,24,27)(18,34,20,32)(26,36,31,35);(5,9,11,10)(6,14,15,24)(7,18,19,20)(8,21,22,23)(12,26,16,31)(13,27,29,28)(17,32,33,34)(25,35,30,36)11234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 13387);