Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C24 |
| direct product | C137×#23847 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C137 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C137 |
| socle | C2×C137 | C2×#401 |
| prime radical | C24×C137 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C137 ◁ C23×C4×C137 ◁ G | |
604 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)(3,11,14,7)(4,8,17,23)(5,9)(6,10)(12,21)(13,25,27,20)(15,19)(16,22,29,32)(18,24)(26,31)(28,30)(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)(2,7)(4,15,17,12)(5,13)(6,14)(8,21,23,19)(9,20)(10,11)(16,28,29,26)(18,27)(22,31,32,30)(24,25);(1,4)(2,8,10,23)(3,12)(5,16)(6,17)(7,19,11,21)(9,22,24,32)(13,26)(14,15)(18,29)(20,30,25,31)(27,28);(1,5,6,18)(2,9,10,24)(3,13,14,27)(4,16,17,29)(7,20,11,25)(8,22,23,32)(12,26,15,28)(19,30,21,31)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 16835);