Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C27×C4 |
| direct product | C83×#60831 |
| 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 ◁ C4×#41×C83 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 generators on 123 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,20)(12,24)(13,19)(14,16)(15,28)(17,22)(18,26)(21,36)(23,32)(25,34)(27,33)(29,30)(31,37)(35,38)(39,40)(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);(1,3,4,8)(2,5,6,7)(10,16)(17,30)(18,24)(19,28)(20,32)(31,40)(33,34)(35,36);(3,8)(5,7)(9,11,14,23)(10,17,16,30)(12,21,26,38)(13,22,15,29)(18,31,24,40)(19,32,28,20)(25,37,27,39)(33,35,34,36);(2,6)(5,7)(9,12)(10,18)(11,21)(13,27)(14,26)(15,25)(16,24)(17,31)(19,34)(20,35)(22,39)(23,38)(28,33)(29,37)(30,40)(32,36);(9,13,14,15)(10,19,16,28)(11,22,23,29)(12,25,26,27)(17,32,30,20)(18,33,24,34)(21,37,38,39)(31,35,40,36)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53819);