Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C137 · Schur multiplier (H2) = C25 |
| direct product | C137×#11048 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #386 |
| commutator | C24 | C22×C4×C137 |
| Frattini, cosocle | C23×C4 | C23×C137 |
| prime radical | C24×C137 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G | |
850 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 3 generators on 173 points:
(2,4)(5,6,9,14,10,13,22,28)(7,11,17,25,16,24,32,35)(8,18,19,29,20,12,21,27)(15,23,31,34,30,26,33,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173);(1,2,3,4)(5,7)(6,11)(8,15)(9,17)(10,16)(12,26)(13,24)(14,25)(18,23)(19,31)(20,30)(21,33)(22,32)(27,36)(28,35)(29,34);(5,8,10,20)(6,12,13,18)(7,15,16,30)(9,21,22,19)(11,23,24,26)(14,29,28,27)(17,33,32,31)(25,36,35,34)6302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 4036);