Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C137 · Schur multiplier (H2) = C22 |
| direct product | C137×#11984 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#102 |
| commutator | C2×C8 | C22×C4×C137 |
| Frattini, cosocle | C4×C8 | C23×C137 |
| prime radical | C23×C137 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ C2×C4×C8×C137 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 3 generators on 177 points:
(2,6)(3,4)(7,8)(9,10,13,19,15,20,28,18,14,17,29,34,27,35,12,26)(11,21,23,31,25,36,39,38,24,37,40,16,30,32,22,33)(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);(1,2)(3,6)(4,8)(5,7)(9,11,14,24)(10,16,17,31)(12,23,28,40)(13,22,29,39)(15,30,27,25)(18,36,26,32)(19,37,34,21)(20,38,35,33);(1,3,5,4)(2,6,7,8)(10,17)(16,31)(18,26)(19,34)(20,35)(21,37)(32,36)(33,38)7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 4972);