Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#19777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C83 |
| prime radical | C83×#3294 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ G | |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 115 points:
(2,6)(4,12)(7,13)(8,9)(10,16)(14,15)(17,18)(19,22)(20,23)(21,25)(24,28)(26,29)(27,31)(30,32)(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);(1,2,5,9)(3,7,11,15)(4,8,12,6)(10,14,16,13)(17,19,21,27)(18,22,25,31)(20,26,28,32)(23,29,24,30);(1,3,5,11)(2,7,9,15)(4,10,12,16)(6,13,8,14)(18,23)(20,28)(22,29)(24,25)(26,32)(30,31);(2,8)(4,12)(6,9)(7,14)(10,16)(13,15)3320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 12765);