Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#21559 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | C2×#121 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| socle | C2×C83 | C4×#121 |
| prime radical | C83×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ C22×C8×C83 ◁ G | |
868 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,12,8,13,7,11)(3,14,5,9,17,24,16,25)(4,18,20,10,21,26,22,27)(15,29,19,28,30,23,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3,6,5,8,17,7,16)(2,9,11,14,13,25,12,24)(4,15,20,19,21,30,22,31)(10,23,18,28,27,29,26,32);(1,4)(2,10)(3,15)(5,19)(6,20)(7,22)(8,21)(9,23)(11,18)(12,26)(13,27)(14,28)(16,31)(17,30)(24,32)(25,29);(1,5,6,17,8,16,7,3)(2,9,12,24,13,25,11,14)(4,19,20,30,21,31,22,15)(10,23,26,32,27,29,18,28)4814 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 14547);