Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#61110 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C73 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G | |
2684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
A minimal faithful permutation representation — 5 generators on 89 points:
(1,2,7,10)(3,12,8,15)(4,14,5,9)(6,13,16,11)(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);(1,3)(2,5)(4,10)(6,9)(7,8)(11,15)(12,13)(14,16);(1,4)(2,8)(3,10)(5,7)(6,15)(9,11)(12,16)(13,14);(1,5)(2,9)(3,13)(4,7)(6,15)(8,11)(10,14)(12,16);(2,10)(3,8)(9,14)(11,13)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54098);