Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C83 · Schur multiplier (H2) = C28 |
| direct product | C83×#61492 |
| 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 | |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 5 generators on 123 points:
(2,5)(6,8)(9,10)(11,16)(12,24)(13,18)(14,28)(15,19)(17,26)(20,36)(21,31)(22,32)(23,38)(25,40)(27,34)(29,35)(30,37)(33,39)(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)(10,16)(12,25)(13,21)(14,23)(15,22)(17,33)(18,31)(19,32)(20,27)(24,40)(26,39)(28,38)(29,37)(30,35)(34,36);(9,12)(10,17)(11,20)(13,26)(14,29)(15,27)(16,30)(18,34)(19,35)(21,37)(22,25)(23,39)(24,28)(31,40)(32,33)(36,38);(2,5)(6,8)(9,13,15,14)(10,18,19,28)(11,21,22,23)(12,26,27,29)(16,31,32,38)(17,34,35,24)(20,37,25,39)(30,40,33,36);(1,3,4,7)(2,6,5,8)(11,22)(16,32)(20,25)(21,23)(30,33)(31,38)(36,40)(37,39)4814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 54480);