Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#19163 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C83 |
| prime radical | C83×#3100 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G | |
760 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,5)(4,7)(6,8)(9,10,13,16)(11,17,18,24)(12,20,21,15)(14,22,23,19)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(9,11,12,19,13,18,21,22)(10,14,15,17,16,23,20,24);(2,5)(3,8)(6,7);(11,18)(14,23)(17,24)(19,22)3569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 12151);