Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#61052 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ #525×C73 ◁ G | |
2722 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 109 points:
(1,2)(3,4)(5,6)(7,15)(8,12)(9,22)(10,13)(11,18)(14,23)(16,29)(17,26)(19,25)(20,33)(21,27)(24,31)(28,34)(30,36)(32,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(5,7,10,19)(6,11,13,26)(8,16,21,32)(9,17,23,18)(12,24,27,36)(14,25,22,15)(20,30,34,31)(28,35,33,29);(2,4)(5,8,10,21)(6,12,13,27)(7,16,19,32)(9,20,23,34)(11,24,26,36)(14,28,22,33)(15,29,25,35)(17,30,18,31);(7,17)(9,23)(11,25)(14,22)(15,26)(16,30)(18,19)(20,34)(24,35)(28,33)(29,36)(31,32);(6,13)(11,26)(12,27)(14,22)(15,25)(24,36)(28,33)(29,35)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 54040);