Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#26925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C23×C137 | H(5,𝔽2) |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C22×C4×C137 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2,4,5)(3,7,8,6)(9,10,14,19,16,12,15,20)(11,21,24,27,26,22,25,17)(13,29,30,28,32,34,31,18)(23,33,37,36,39,40,38,35)(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);(2,5)(6,7)(9,11,16,26)(10,17,12,27)(13,23,32,39)(14,25,15,24)(18,33,28,40)(19,22,20,21)(29,35,34,36)(30,38,31,37);(9,12,16,10)(11,22,26,21)(13,28,32,18)(14,19,15,20)(17,24,27,25)(23,36,39,35)(29,31,34,30)(33,38,40,37);(1,3,4,8)(2,6,5,7)(9,13)(10,18)(11,23)(12,28)(14,31)(15,30)(16,32)(17,33)(19,34)(20,29)(21,35)(22,36)(24,38)(25,37)(26,39)(27,40)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 19913);