Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#20553 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C22 | C22×C42×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C23×C73 | C23×C4 |
| prime radical | C24×C73 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2,3,4)(5,6)(7,10)(8,9)(11,12)(13,14,17,21,19,22,18,15)(16,20,26,24,25,28,27,23)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(6,9)(7,11)(13,15,18,22,19,21,17,14)(16,24,27,20,25,23,26,28);(5,7,8,11)(6,10,9,12)(13,16)(14,20)(15,23)(17,26)(18,27)(19,25)(21,24)(22,28);(6,9)(10,12)(16,25)(20,28)(23,24)(26,27)6424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 13541);