Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#9084 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C83 |
| Frattini, cosocle | C23×C4 | C23×C83 |
| prime radical | C25×C83 | C2×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G | |
712 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)(5,6,9,11,8,7,10,12)(13,14,17,20,18,19,16,15)(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);(5,7,9,12,8,6,10,11)(13,15,17,19,18,20,16,14);(2,4)(6,7)(11,12)(13,16,18,17)(14,15,19,20)4316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 2072);