Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C4×D4×C137 ◁ C8×D4×C137 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 4 generators on 173 points:
(1,2)(3,4)(5,6,12,8)(7,17,19,32)(9,23,26,15)(10,22,29,14)(11,24,28,16)(13,25,18,20)(21,35,30,33)(27,34,36,31)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173);(5,7,12,19)(6,13,8,18)(9,25,26,20)(10,27,29,36)(11,30,28,21)(14,32,22,17)(15,33,23,35)(16,34,24,31);(2,4)(5,8,12,6)(7,18,19,13)(9,22,26,14)(10,23,29,15)(11,24,28,16)(17,20,32,25)(21,34,30,31)(27,35,36,33);(5,9)(6,14)(7,19)(8,22)(10,28)(11,29)(12,26)(13,18)(15,24)(16,23)(17,35)(20,36)(25,27)(32,33)7535 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26838);