Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#61763 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| prime radical | C83×#3539 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #525×C83 ◁ G | |
1692 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 generators on 131 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18)(19,24)(20,32)(21,26)(22,35)(23,27)(25,33)(28,43)(29,38)(30,39)(31,40)(34,41)(36,42)(37,44)(45,48)(46,47)(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);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19,23,31)(18,24,27,40)(20,28,34,46)(21,29,22,30)(25,37,42,48)(26,38,35,39)(32,43,41,47)(33,44,36,45);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20,23,34)(18,25,27,42)(19,28,31,46)(21,33,22,36)(24,37,40,48)(26,41,35,32)(29,44,30,45)(38,47,39,43);(3,11)(6,9)(10,16)(13,15)(17,21,23,22)(18,26,27,35)(19,29,31,30)(20,33,34,36)(24,38,40,39)(25,41,42,32)(28,44,46,45)(37,47,48,43);(2,8)(6,9)(7,14)(13,15)(17,21,23,22)(18,26,27,35)(19,30,31,29)(20,33,34,36)(24,39,40,38)(25,41,42,32)(28,45,46,44)(37,43,48,47)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 54751);