Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C26×C4 |
| direct product | C83×#20983 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C83 |
| Frattini, cosocle | C24 | C24×C83 |
| socle | C22×C83 | C22×C22⋊C4 |
| prime radical | C2×#525×C83 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C24×C4×C83 ◁ G | |
1994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,4)(5,6)(7,10,14,17)(8,11)(9,12)(13,16,19,20)(15,18)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(5,7)(6,10,12,17)(8,13)(9,14)(11,16,18,20)(15,19);(2,4);(5,8,9,15)(6,11,12,18)(7,13,14,19)(10,16,17,20)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13971);