Finite Group DatabasebetaFinite Group Databasebeta| order | 30861 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C127 · Schur multiplier (H2) = C3 |
| direct product | C127×#6897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C127 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C127 |
| prime radical | C33×C127 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C127 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 10287 |
A minimal faithful permutation representation — 3 generators on 181 points:
(1,2,6)(3,10,23)(4,8,16)(5,9,17)(7,18,14)(11,20,26)(12,19,27)(13,21,24)(15,22,25)(28,29,32)(30,33,39)(31,35,40)(34,44,38)(36,41,47)(37,43,48)(42,51,46)(45,50,53)(49,54,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181);(1,3,11,5,4,12,15,14,13)(2,7,19,9,10,21,22,8,20)(6,16,24,17,18,26,25,23,27)(28,30,36,31,37,45,38,46,52)(29,33,41,35,43,50,34,42,49)(32,39,47,40,48,53,44,51,54);(1,4,13,5,14,11,15,3,12)(2,8,21,9,7,20,22,10,19)(6,16,24,17,18,26,25,23,27)(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54)6477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30861, 44);