Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#62168 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| prime radical | #121×C83 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #529×C83 ◁ G | |
1628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 generators on 131 points:
(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18)(19,27)(20,31)(21,25)(22,35)(23,29)(24,33)(26,34)(28,43)(30,38)(32,40)(36,39)(37,47)(41,45)(42,46)(44,48)(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)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,23)(20,28)(21,29)(22,30)(24,37)(25,27)(26,38)(31,48)(32,44)(33,45)(34,46)(35,42)(36,47)(39,41)(40,43);(17,20,21,32)(18,24,25,39)(19,28,29,44)(22,36,34,33)(23,37,27,41)(26,40,35,31)(30,47,46,45)(38,43,42,48);(3,10)(6,9)(11,16)(14,15)(19,29)(23,27)(28,44)(30,46)(37,41)(38,42)(43,48)(45,47);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(18,25)(19,29)(24,39)(26,35)(28,44)(30,46)(31,40)(45,47)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 55156);