Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C137 · Schur multiplier (H2) = C23 |
| direct product | C137×#9331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #386 |
| commutator | C22×C4 | C22×C4×C137 |
| Frattini, cosocle | C23×C4 | C23×C137 |
| prime radical | #525×C137 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
438 conjugacy classes of subgroups.
| minimal degree | μ(G) = 185 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 3 generators on 185 points:
(1,2)(3,6,10,14)(4,11,12,7)(5,8)(9,13)(15,16)(17,18)(19,28)(20,32,35,42)(21,36)(22,26)(23,27)(24,30)(25,34,41,33)(29,44,46,38)(31,39)(37,40)(43,45,48,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185);(1,3)(2,6,8,14)(4,9)(5,10)(7,13,11,16)(12,15)(17,19,21,30,23,31,22,37)(18,24,26,28,27,40,36,39)(20,29,34,47,35,46,33,45)(25,38,42,43,41,44,32,48);(1,4)(2,7)(3,9)(5,12)(6,13)(8,11)(10,15)(14,16)(17,20)(18,25)(19,29)(21,34)(22,33)(23,35)(24,38)(26,42)(27,41)(28,43)(30,47)(31,46)(32,36)(37,45)(39,48)(40,44)4658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 2319);