Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C25 |
| direct product | C73×#22897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | D42 |
| commutator | C2×C4 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#453×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,4,3)(5,6)(7,16)(8,12)(9,14)(10,13)(11,15)(17,20)(18,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,4,2)(5,7,11,17)(6,8,15,18)(9,19,10,12)(13,20,14,16);(5,8,11,18)(6,7,15,17)(9,16,10,20)(12,14,19,13);(5,8)(6,12)(7,13)(9,20)(10,16)(11,18)(14,17)(15,19)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15885);