Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#8946 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C2×D4 |
| commutator | C2×C4 | C22×C8×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| socle, prime radical | C23×C73 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ C2×C4×C8×C73 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 101 points:
(2,4)(5,6,8,11,9,7,10,12)(14,18,20,23)(15,21,22,24)(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);(1,2,3,4)(5,7,8,12,9,6,10,11)(13,14,16,23,17,20,25,18)(15,19,24,27,22,28,21,26);(13,15,17,22)(14,19,20,28)(16,24,25,21)(18,26,23,27)5548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1934);