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×#20438 |
| 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 | C24×C83 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C83 ◁ G | |
1110 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)(9,10,13,12,14,16,21,20)(11,15,19,17,18,22,24,23)(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)(5,6,7,8)(9,11)(10,15)(12,17)(13,19)(14,18)(16,22)(20,23)(21,24);(9,12,13,16,14,20,21,10)(11,17,19,22,18,23,24,15);(11,18)(15,22)(17,23)(19,24)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 13426);