Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C27 |
| direct product | C137×#23885 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C22×C4×C137 ◁ G | |
1662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2)(3,14)(4,19)(5,22)(6,12)(7,11)(8,13)(9,17)(10,21)(15,24)(16,25)(18,28)(20,27)(23,26)(29,31)(30,32)(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)(2,9)(4,15)(5,16)(6,23)(7,17)(8,18)(10,25)(11,28)(12,14)(13,26)(19,29)(20,32)(21,31)(22,30)(24,27);(1,4,8,5)(2,10,13,27)(3,15,18,16)(6,21,7,20)(9,24,26,25)(11,19,12,22)(14,29,28,30)(17,32,23,31);(1,5,8,4)(2,10,13,27)(3,16,18,15)(6,20,7,21)(9,25,26,24)(11,19,12,22)(14,30,28,29)(17,31,23,32)5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 16873);