Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#13026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #447 |
| commutator | C2×C8 | C22×C4×C73 |
| Frattini, cosocle | C22×C8 | C23×C73 |
| prime radical | C2×#135×C73 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#97×C73 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 109 points:
(2,4)(5,6,9,14,24,33,25,34,11,16,8,13,10,15,26,35)(7,17,19,29,27,32,22,12,21,28,18,36,20,31,23,30)(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);(1,2,3,4)(5,7)(6,12)(8,22)(9,23)(10,27)(11,21)(13,31)(14,32)(15,36)(16,30)(17,34)(18,25)(19,26)(20,24)(28,35)(29,33);(5,7)(6,12)(8,23)(9,22)(10,27)(11,21)(13,32)(14,31)(15,36)(16,30)(17,35)(18,26)(19,25)(20,24)(28,34)(29,33)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 6014);