Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C137 · Schur multiplier (H2) = C22 |
| direct product | C2×M128×C137 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C137 | C22 |
| commutator | C2 | C22×C32×C137 |
| Frattini, cosocle | C32 | C23×C137 |
| socle | C22×C137 | C2×C32 |
| prime radical | C23×C137 | C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C137 ◁ G | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 203 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 3 generators on 203 points:
(1,2)(67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203);(3,4,5,11,6,12,15,29,7,13,16,30,19,32,35,51,8,14,17,31,20,33,36,52,22,34,38,53,41,54,55,64,9,10,18,25,21,26,37,45,23,27,39,46,42,48,56,60,24,28,40,47,43,49,57,61,44,50,58,62,59,63,65,66);(4,10)(11,25)(12,26)(13,27)(14,28)(29,45)(30,46)(31,47)(32,48)(33,49)(34,50)(51,60)(52,61)(53,62)(54,63)(64,66)21920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 6724);