Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C137 · Schur multiplier (H2) = C24×C4 |
| direct product | C137×#21883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C24×C137 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×#117×C137 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 4 generators on 177 points:
(2,5)(3,7)(9,10,14,18,13,17,27,34)(11,19,22,36,21,15,29,31)(12,23,26,35,25,16,28,33)(20,30,37,39,24,32,38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(1,2)(3,6)(4,5)(7,8)(9,11)(10,15)(12,24)(13,21)(14,22)(16,32)(17,19)(18,31)(20,25)(23,30)(26,38)(27,29)(28,37)(33,40)(34,36)(35,39);(2,5)(6,8)(9,12,13,25)(10,16,17,23)(11,20,21,24)(14,28,27,26)(15,30,19,32)(18,35,34,33)(22,38,29,37)(31,40,36,39);(1,3,4,7)(2,6,5,8)(10,17)(11,21)(16,23)(18,34)(20,24)(22,29)(33,35)(37,38)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 14871);