Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#19406 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C83 |
| prime radical | #532×C83 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,10)(4,8)(5,14)(6,9)(7,12)(11,15)(13,16)(17,18,23,26)(19,21,25,22)(20,27,30,31)(24,29,32,28)(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);(1,3,5,12,6,13,4,11)(2,7,8,10,9,15,14,16)(17,19,22,18,23,25,21,26)(20,27,29,24,30,31,28,32);(17,20,23,30)(18,24,26,32)(19,27,25,31)(21,28,22,29);(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,10,15,16)(17,21,23,22)(18,25,26,19)(20,28,30,29)(24,31,32,27)4067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 12394);