Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C113 · Schur multiplier (H2) = C25 |
| direct product | C113×#18970 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C113 |
| prime radical | C113×#3554 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 14464 |
A minimal faithful permutation representation — 4 generators on 161 points:
(1,2)(3,7)(4,6)(5,9)(8,12)(10,14)(11,13)(15,16)(17,18,23,28)(19,24,31,39)(20,32,34,42)(21,27,22,26)(25,36,40,33)(29,43,45,47)(30,41,35,38)(37,44,48,46)(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);(2,6)(4,12)(7,13)(8,9)(11,16)(14,15)(17,19)(18,24)(20,29)(21,30)(22,35)(23,31)(25,37)(26,38)(27,41)(28,39)(32,47)(33,44)(34,45)(36,46)(40,48)(42,43);(1,3,5,10)(2,7,9,14)(4,11,12,16)(6,13,8,15)(17,20)(18,25)(19,29)(21,33)(22,36)(23,34)(24,37)(26,32)(27,42)(28,40)(30,44)(31,45)(35,46)(38,47)(39,48)(41,43);(3,10)(7,14)(11,16)(13,15)(17,21,23,22)(18,26,28,27)(19,30,31,35)(20,33,34,36)(24,38,39,41)(25,32,40,42)(29,44,45,46)(37,47,48,43)4181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 11958);