Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#33633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C137 |
| prime radical | C2×#135×C137 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ #117×C137 ◁ #405×C137 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,18)(13,26)(14,30)(15,20)(17,22)(19,28)(21,31)(23,34)(24,33)(25,37)(27,32)(29,40)(35,39)(36,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(1,3,4,8)(2,5,6,7)(9,11)(10,16)(12,24)(13,22)(14,21)(15,23)(17,26)(18,33)(19,32)(20,34)(25,39)(27,28)(29,38)(30,31)(35,37)(36,40);(9,11)(10,17)(12,21)(13,27)(14,24)(15,23)(16,26)(18,32)(19,33)(20,36)(22,28)(25,38)(29,39)(30,35)(31,37)(34,40);(9,12,15,14)(10,18,20,30)(11,21,23,24)(13,25,29,28)(16,31,34,33)(17,32,36,35)(19,26,37,40)(22,27,38,39)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26621);