Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C83 · Schur multiplier (H2) = C25×C4 |
| direct product | C83×#20416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C22×D4 |
| commutator | C4 | C22×C42×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| prime radical | C23×D4×C83 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×#117×C83 ◁ G | |
1738 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)(3,4)(5,6,8,7)(9,10)(11,19)(12,16)(13,17)(14,18)(15,20)(21,24)(22,23)(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);(2,4)(9,11,13,21,14,22,12,20)(10,15,16,23,18,24,17,19);(5,7,8,6)(9,10)(11,15)(12,17)(13,16)(14,18)(19,20)(21,23)(22,24);(9,12,14,13)(10,16,18,17)(11,20,22,21)(15,23,24,19)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13404);