Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C83 · Schur multiplier (H2) = C213 |
| direct product | C83×#62805 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C83 |
| socle | C22×C83 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ G | |
7104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 6 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,16)(11,17,18,14)(12,20,21,15)(19,22,24,23)(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);(2,5)(6,8);(9,11)(10,14)(12,19)(13,18)(15,22)(16,17)(20,23)(21,24);(11,18)(14,17)(19,24)(22,23);(9,12,13,21)(10,15,16,20)(11,19,18,24)(14,22,17,23);(1,3,4,7)(2,6,5,8)7304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 55793);