Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#12685 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C83 | #120 |
| commutator | C2×C4 | C22×C8×C83 |
| Frattini, cosocle | C22×C8 | C23×C83 |
| socle | C2×C83 | #1779 |
| prime radical | #585×C83 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C83 ◁ C22×C8×C83 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 147 points:
(1,2,6,12,7,13,27,40,8,14,28,41,5,11,25,38)(3,15,19,43,17,31,49,39,18,36,26,54,23,9,29,32)(4,10,21,34,20,33,50,59,22,35,52,61,24,37,53,62)(16,44,47,64,48,30,56,58,46,42,51,63,45,57,55,60)(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);(1,3)(2,9)(4,16)(5,23)(6,26)(7,17)(8,18)(10,30)(11,36)(12,39)(13,15)(14,31)(19,28)(20,48)(21,51)(22,46)(24,45)(25,49)(27,29)(32,41)(33,42)(34,60)(35,57)(37,44)(38,43)(40,54)(47,52)(50,55)(53,56)(58,61)(59,64)(62,63);(1,4)(2,10)(3,16)(5,24)(6,21)(7,20)(8,22)(9,30)(11,37)(12,34)(13,33)(14,35)(15,42)(17,48)(18,46)(19,47)(23,45)(25,53)(26,51)(27,50)(28,52)(29,55)(31,57)(32,58)(36,44)(38,62)(39,60)(40,59)(41,61)(43,63)(49,56)(54,64)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 5673);