Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#17429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C2×#127×C83 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C4×D4×C83 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2)(3,9,11,6)(4,7)(5,8)(10,15,16,13)(12,14)(17,18,21,26,22,25,20,24)(19,27,28,32,29,23,30,31)(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);(1,3,5,11)(2,6,8,9)(4,10,12,16)(7,13,14,15)(17,19,22,29)(18,23,25,27)(20,28,21,30)(24,31,26,32);(1,4)(2,7)(3,10)(5,12)(6,13)(8,14)(9,15)(11,16)(17,20,22,21)(18,24,25,26)(19,28,29,30)(23,31,27,32);(4,12)(7,14)(10,16)(13,15)(17,20,22,21)(18,24,25,26)(19,28,29,30)(23,31,27,32)4565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10417);