Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#33843 |
| 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 | |
668 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)(6,11)(7,15)(8,19)(9,22)(12,27)(13,30)(14,33)(16,29)(17,31)(18,25)(20,24)(23,26)(28,32)(34,35)(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);(5,6,10,12)(7,16,18,30)(8,20,23,33)(9,24,22,14)(11,26,27,19)(13,31,29,17)(15,35,25,28)(21,34,36,32);(2,4)(6,12)(11,27)(13,29)(14,24)(16,30)(20,33)(28,35)(32,34);(5,7,10,18)(6,13,12,29)(8,21,23,36)(9,25,22,15)(11,28,27,35)(14,34,24,32)(16,33,30,20)(17,26,31,19)5891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 26831);