Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C137 · Schur multiplier (H2) = C27 |
| direct product | C137×#23884 |
| 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 | |
1684 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)(3,13)(4,17)(5,11)(6,9)(7,12)(8,15)(10,18)(14,22)(16,24)(19,26)(20,25)(21,23)(27,28)(29,32)(30,31)(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)(2,8)(4,14)(5,21)(6,15)(7,16)(9,24)(10,22)(11,13)(12,23)(17,27)(18,30)(19,28)(20,29)(25,31)(26,32);(2,9)(5,6)(8,13)(10,25)(11,12)(15,21)(17,26)(18,19)(22,27)(23,24)(28,30)(31,32);(1,4,7,20)(2,10,12,26)(3,14,16,29)(5,19,6,18)(8,22,23,32)(9,25,11,17)(13,27,24,31)(15,30,21,28)5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 16872);