Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#18419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C83×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G | |
1062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,11)(3,13,16,29)(4,10,5,20)(7,12,23,28)(8,21,26,14)(9,22,18,19)(15,24,17,31)(25,30,27,32)(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)(2,8)(4,14)(5,21)(6,16)(7,17)(9,24)(10,29)(11,26)(12,27)(13,20)(15,23)(18,31)(19,30)(22,32)(25,28);(1,2)(3,8)(4,18)(5,9)(6,11)(7,12)(10,22)(13,30)(14,31)(15,25)(16,26)(17,27)(19,20)(21,24)(23,28)(29,32);(1,4,6,5)(2,9,11,18)(3,14,16,21)(7,19,23,22)(8,24,26,31)(10,28,20,12)(13,27,29,25)(15,32,17,30)3071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 11407);