Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#22037 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C73 | C24 |
| commutator | C23 | C23×C4×C73 |
| Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C23×C73 | C23×C4 |
| prime radical | C73×#2388 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C73 ◁ G | |
1034 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)(7,11)(8,10)(9,12)(13,14,18,15,17,20,26,22)(16,19,25,21,24,27,28,23)(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);(5,7)(6,9)(8,12)(10,11)(13,15,18,20,17,22,26,14)(16,23,25,19,24,21,28,27);(2,4)(7,12)(9,11)(13,16)(14,19)(15,21)(17,24)(18,25)(20,27)(22,23)(26,28);(6,10)(9,11)(14,20)(15,22)(16,24)(25,28)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 15025);