Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#9955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C83 |
| prime radical | C23×D4×C83 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2)(3,5)(4,6)(7,8)(9,10,14,18)(11,19,21,23)(12,15,13,17)(16,22,24,20)(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);(5,8)(10,15)(12,13)(16,19)(17,18)(20,22)(23,24);(1,3)(2,5)(4,7)(6,8)(9,11,14,21)(10,16,18,24)(12,20,13,22)(15,23,17,19)3071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 2943);