Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C101 · Schur multiplier (H2) = C23 |
| direct product | C101×#13406 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C101 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C101 |
| socle | C2×C101 | #2034 |
| prime radical | C101×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ C22×C4×C101 ◁ C2×#131×C101 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 165 points:
(1,2)(3,14)(4,20)(5,12)(6,28)(7,13)(8,16)(9,23)(10,27)(11,26)(15,46)(17,33)(18,35)(19,34)(21,54)(22,55)(24,41)(25,53)(29,40)(30,39)(31,42)(32,51)(36,62)(37,58)(38,59)(43,57)(44,48)(45,52)(47,64)(49,63)(50,61)(56,60)(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);(1,3)(2,8)(4,21)(5,18)(6,29)(7,19)(9,36)(10,34)(11,40)(12,14)(13,35)(15,24)(16,27)(17,31)(20,46)(22,49)(23,56)(25,47)(26,50)(28,45)(30,48)(32,37)(33,43)(38,44)(39,60)(41,64)(42,61)(51,59)(52,57)(53,63)(54,55)(58,62);(1,4,7,25)(2,9,13,38)(3,15)(5,24,27,22)(6,30,31,58)(8,32)(10,39,12,37)(11,41,43,55)(14,44)(16,21)(17,51)(18,47)(19,49)(20,42,53,28)(23,57,59,26)(29,56)(33,46)(34,36)(35,60)(40,63)(45,64)(48,52)(50,62)(54,61)4040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 6394);