Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C73×#33526 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×#41×C73 ◁ C2×#131×C73 ◁ G | |
1150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 109 points:
(1,2)(3,4)(5,6)(7,13)(8,14)(9,22)(10,26)(11,16)(12,18)(15,24)(17,30)(19,32)(20,31)(21,33)(23,27)(25,36)(28,35)(29,34)(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)(6,12)(8,17)(9,23)(10,20)(11,19)(13,22)(14,27)(15,31)(16,29)(18,24)(21,34)(25,35)(26,28)(30,33)(32,36);(2,4)(5,7)(6,13)(8,20)(9,18)(10,17)(11,19)(12,22)(14,31)(15,27)(16,32)(21,35)(23,24)(25,34)(26,30)(28,33)(29,36);(5,8,11,10)(6,14,16,26)(7,17,19,20)(9,21,25,24)(12,27,29,28)(13,30,32,31)(15,22,33,36)(18,23,34,35)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26514);