Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C25 |
| direct product | C139×#33982 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | C22×D16 |
| commutator, Frattini, cosocle | C16 | C24×C139 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ #41×C139 ◁ #131×C139 ◁ #504×C139 ◁ G | |
472 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 203 |
| transitive degree | μt(G) = 8896 |
A minimal faithful permutation representation — 4 generators on 203 points:
(1,2)(3,9)(4,8)(5,22)(6,25)(7,13)(10,18)(11,19)(12,23)(14,30)(15,26)(16,44)(17,45)(20,37)(21,29)(24,51)(27,47)(28,46)(31,41)(32,42)(33,40)(34,50)(35,48)(36,49)(38,52)(39,62)(43,58)(53,63)(54,61)(55,59)(56,60)(57,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203);(2,8)(4,18)(5,19)(6,23)(9,26)(10,11)(12,37)(13,29)(15,41)(16,42)(17,40)(20,50)(21,48)(22,27)(24,49)(25,28)(30,52)(31,32)(33,58)(34,51)(35,36)(38,59)(39,60)(43,64)(44,53)(45,54)(46,47)(55,56)(57,62)(61,63);(1,3)(2,9)(4,15)(5,16)(6,17)(7,14)(8,26)(10,31)(11,32)(12,33)(13,30)(18,41)(19,42)(20,43)(21,38)(22,44)(23,40)(24,39)(25,45)(27,53)(28,54)(29,52)(34,57)(35,55)(36,56)(37,58)(46,61)(47,63)(48,59)(49,60)(50,64)(51,62);(3,14)(9,30)(15,38)(16,39)(17,40)(26,52)(31,55)(32,56)(33,45)(41,59)(42,60)(43,61)(44,62)(53,57)(54,58)(63,64)7228 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 26970);