Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C83 · Schur multiplier (H2) = C23×C42 |
| direct product | C83×#20370 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C83 | C22×C42 |
| commutator | C4 | C22×C42×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| socle | C2×C83 | C2×#376 |
| prime radical | C24×C83 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C83 ◁ G | |
908 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)(3,11,14,24)(4,8)(5,9)(6,10)(7,13,19,27)(12,23,25,31)(15,20)(16,21)(17,22)(18,26,29,32)(28,30)(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)(2,7,10,19)(4,12)(5,13)(6,14)(8,18,20,29)(9,11,22,24)(15,25)(16,26)(17,27)(21,23,30,31)(28,32);(1,4,5,16,6,15,17,28)(2,8,9,21,10,20,22,30)(3,12,13,26,14,25,27,32)(7,18,11,23,19,29,24,31);(4,15)(8,20)(12,25)(16,28)(18,29)(21,30)(23,31)(26,32)6806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13358);