Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22×C4 |
| direct product | C73×#9733 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | #121 |
| commutator | C42 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G | |
518 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 101 points:
(2,4)(5,6,7,10,8,11,12,9)(13,14)(15,20)(16,25)(17,27)(18,22)(19,23)(21,26)(24,28)(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)(7,12)(10,11)(13,15,17,23,18,24,26,16)(14,19,21,20,22,25,27,28);(13,16,26,24,18,23,17,15)(14,20,27,19,22,28,21,25)4234 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2721);