Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#10350 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,13)(12,15)(14,16)(18,22)(19,20)(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);(1,3,4,8)(2,5,6,7)(18,23)(19,20)(22,24);(10,13)(11,16)(14,15)(17,18,21,24)(19,23,20,22)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 3338);