Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#61862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| prime radical | #449×C83 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #533×C83 ◁ G | |
1614 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)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,22,27)(19,29,31,24)(20,33,35,42)(21,28,23,26)(25,37,40,34)(30,44,45,48)(32,39,36,41)(38,47,43,46)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19,22,31)(18,24,27,29)(20,30,35,45)(21,36,23,32)(25,38,40,43)(26,41,28,39)(33,48,42,44)(34,47,37,46);(17,20)(18,25)(19,30)(21,34)(22,35)(23,37)(24,38)(26,33)(27,40)(28,42)(29,43)(31,45)(32,46)(36,47)(39,44)(41,48);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(19,31)(24,29)(30,45)(32,36)(38,43)(39,41)(44,48)(46,47);(2,8)(6,9)(7,16)(14,15)(17,21,22,23)(18,26,27,28)(19,32,31,36)(20,34,35,37)(24,39,29,41)(25,33,40,42)(30,46,45,47)(38,44,43,48)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 54850);