Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C27×C4 |
| direct product | C83×#60819 |
| 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 | |
2058 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 5 generators on 123 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,20)(12,24)(13,18)(14,16)(15,21)(17,25)(19,27)(22,29)(23,28)(26,32)(30,35)(31,37)(33,34)(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);(1,3,4,8)(2,5,6,7)(9,11)(10,15)(12,22)(13,21)(14,23)(16,30)(17,29)(18,20)(19,28)(24,33)(25,34)(26,36)(27,35)(31,39)(32,38)(37,40);(3,8)(5,7)(10,16)(11,21)(14,27)(15,28)(17,31)(18,19)(20,30)(22,34)(24,32)(26,37)(29,38)(33,39);(2,6)(5,7)(9,12)(10,17)(11,22)(13,25)(14,26)(15,29)(16,31)(18,24)(19,32)(20,33)(21,34)(23,36)(27,37)(28,38)(30,39)(35,40);(12,25)(17,24)(22,34)(26,37)(29,33)(31,32)(36,40)(38,39)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 53807);