Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C32×C73 |
| multiplicative | (ℤ/37504)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C16 | C23×C73 |
| socle, prime radical | C23×C73 | C2×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(33,34,35,36);(37,38)18688 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6534);