Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C83 · Schur multiplier (H2) = C24×C4 |
| direct product | C83×#20492 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C83 | C24 |
| commutator | C22 | C22×C42×C83 |
| Frattini, cosocle | C22×C4 | C24×C83 |
| socle | C23×C83 | C23×C4 |
| prime radical | C22×D4×C83 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C83 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,4)(9,10,14,17,13,16,22,24)(11,18,20,21,19,15,23,12)(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)(5,6,8,7)(9,11)(10,15)(12,17)(13,19)(14,20)(16,18)(21,24)(22,23);(5,7,8,6)(11,19)(12,21)(15,18)(20,23);(9,12,14,18,13,21,22,15)(10,11,17,20,16,19,24,23)8300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13480);