Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#62012 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C83 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ #529×C83 ◁ G | |
1792 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 generators on 123 points:
(2,5)(3,7)(9,10)(11,16)(12,24)(13,18)(14,27)(15,19)(17,25)(20,34)(21,30)(22,31)(23,37)(26,32)(28,33)(29,35)(36,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,2)(3,6)(4,5)(7,8)(9,11,15,22)(10,16,19,31)(12,20,26,36)(13,21,14,23)(17,29,33,40)(18,30,27,37)(24,34,32,39)(25,35,28,38);(9,12)(10,17)(11,20)(13,25)(14,28)(15,26)(16,29)(18,32)(19,33)(21,35)(22,36)(23,38)(24,27)(30,39)(31,40)(34,37);(2,5)(6,8)(9,13,15,14)(10,18,19,27)(11,21,22,23)(12,25,26,28)(16,30,31,37)(17,32,33,24)(20,35,36,38)(29,39,40,34);(1,3,4,7)(2,6,5,8)(11,22)(16,31)(20,36)(21,23)(29,40)(30,37)(34,39)(35,38)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 55000);