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×#9138 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C73 |
| Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C24×C73 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C22×C42×C73 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2)(3,4)(6,9)(7,10)(11,12)(13,14,17,22,18,21,16,20)(15,19,25,27,24,28,23,26)(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);(5,6,10,12,8,11,7,9)(13,15,16,25,18,24,17,23)(14,19,22,26,21,28,20,27);(2,4)(6,11)(9,12)(13,16,18,17)(14,20,21,22)(15,23,24,25)(19,26,28,27)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2126);