Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#12988 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C137 | #386 |
| commutator | C2×C4 | C22×C8×C137 |
| Frattini, cosocle | C22×C8 | C23×C137 |
| socle | C2×C137 | #1869 |
| prime radical | #532×C137 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C137 ◁ C22×C8×C137 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 3 generators on 169 points:
(1,2,6,12,7,10,24,27,8,11,25,29,5,22,14,31)(3,13,17,23,18,28,32,4,16,20,30,19,15,9,26,21)(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);(1,3,14,26,5,15,25,30,8,16,24,32,7,18,6,17)(2,9,27,23,22,20,12,21,11,28,31,19,10,13,29,4);(1,4)(2,3)(5,23)(6,13)(7,19)(8,21)(9,14)(10,18)(11,16)(12,30)(15,22)(17,29)(20,25)(24,28)(26,27)(31,32)7946 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 5976);