Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#61801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| prime radical | C83×#3551 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #532×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)(19,23)(20,25)(21,24)(22,27)(26,34)(28,36)(29,37)(30,35)(31,40)(32,41)(33,39)(38,44)(42,46)(43,47)(45,48)(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)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,23)(20,31)(21,30)(22,29)(24,35)(25,40)(26,38)(27,37)(28,32)(33,45)(34,44)(36,41)(39,48)(42,47)(43,46);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(18,24)(21,34)(23,35)(25,39)(26,27)(30,44)(33,46)(36,47)(37,38)(40,48)(41,42)(43,45);(3,11)(6,9)(10,16)(13,15)(17,20)(18,25)(19,28)(21,33)(22,32)(23,36)(24,39)(26,42)(27,41)(29,31)(30,43)(34,46)(35,47)(37,40)(38,48)(44,45);(2,8)(6,9)(7,14)(13,15)(19,29)(20,32)(23,37)(25,41)(30,44)(33,46)(35,38)(39,42)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 54789);