Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C23×C4 |
| direct product | C73×#24665 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| prime radical | C2×#121×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G | |
856 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 generators on 101 points:
(5,6)(7,11)(8,9)(10,12)(13,14,18,23,19,24,17,22)(15,20,25,21,16,26,27,28)(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);(1,2)(3,4)(6,9)(10,11)(13,15)(14,20)(16,19)(17,27)(18,25)(21,23)(22,28)(24,26);(2,4)(13,16,19,15)(14,21,24,28)(17,27,18,25)(20,22,26,23);(5,7,8,12)(6,10,9,11)(13,17,19,18)(14,22,24,23)(15,25,16,27)(20,21,26,28)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17653);