Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C25 |
| direct product | C83×#8405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #120 |
| commutator | C22×C4 | C22×C4×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| prime radical | C25×C83 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2)(3,4)(5,6)(7,8,11,12)(9,10)(13,14,17,20,18,15,16,19)(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);(2,4)(5,7)(6,8)(9,11)(10,12)(13,15,18,14)(16,19,17,20);(5,8)(6,7)(9,12)(10,11)3818 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 1393);