Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C26 |
| direct product | C137×#32951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C137 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C22×C4×C137 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4384 |
A minimal faithful permutation representation — 4 generators on 169 points:
(2,7)(3,12)(5,8)(10,20)(11,21)(13,28)(14,15)(16,17)(19,23)(22,31)(25,26)(27,29)(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);(1,2,8,21,6,11,5,7)(3,9,12,23,15,24,14,19)(4,10,17,25,18,26,16,20)(13,22,27,32,29,31,28,30);(1,3)(2,9)(4,13)(5,14)(6,15)(7,19)(8,12)(10,22)(11,24)(16,28)(17,27)(18,29)(20,30)(21,23)(25,32)(26,31);(1,4)(2,10)(3,13)(5,16)(6,18)(7,20)(8,17)(9,22)(11,26)(12,27)(14,28)(15,29)(19,30)(21,25)(23,32)(24,31)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 25939);