Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#29232 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2572 |
| prime radical | #575×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
A minimal faithful permutation representation — 4 generators on 89 points:
(1,2,5,9,6,10,4,7)(3,11,12,16,13,8,14,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(2,7,10,9)(3,12,13,14)(8,11)(15,16);(1,3)(2,8)(4,12)(5,14)(6,13)(7,15)(9,16)(10,11);(2,7,10,9)(8,15,11,16)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 22220);