Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#18744 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| prime radical | #3212×C137 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
852 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2)(3,9)(4,6)(5,13)(7,11)(8,15)(10,14)(12,16)(18,23)(19,26)(20,21)(25,29)(27,28)(30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,3,6,12)(2,7,4,10)(5,14,15,11)(8,16,13,9)(17,18,22,25)(19,24,28,32)(20,23,21,29)(26,30,27,31);(1,4,6,2)(3,10,12,7)(5,13,15,8)(9,11,16,14)(17,19,22,28)(18,24,25,32)(20,26,21,27)(23,30,29,31);(2,4)(7,10)(8,13)(9,16)(17,20,22,21)(18,23,25,29)(19,27,28,26)(24,31,32,30)5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 11732);