Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C137 · Schur multiplier (H2) = C26 |
| direct product | C137×#22455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C137 |
| Frattini, cosocle | C22×C4 | C24×C137 |
| prime radical | C2×#576×C137 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C22×C4×C137 ◁ G | |
1378 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)(4,16,18,8)(5,19)(6,10)(7,14)(9,20)(12,26,29,25)(13,23)(15,22)(17,24,32,31)(21,28,30,27)(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)(4,12)(5,13)(6,15)(8,21)(9,22)(10,23)(11,19)(14,20)(16,30)(17,27)(18,29)(24,26)(25,31)(28,32);(1,4)(2,8)(3,12)(5,17)(6,18)(7,21)(9,24)(10,16)(11,25)(13,27)(14,28)(15,29)(19,31)(20,32)(22,26)(23,30);(3,13)(5,20)(7,22)(9,19)(11,23)(12,27)(14,15)(17,32)(21,26)(24,31)(25,30)(28,29)7124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 15443);