Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C73 · Schur multiplier (H2) = C22 |
| direct product | C2×C73×#1366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #333 |
| commutator | C42 | C22×C4×C73 |
| Frattini, cosocle | C4×C8 | C23×C73 |
| prime radical | C23×C73 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×C4×C8×C73 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(3,4,6,11,19,12,30,28,8,13,21,29,7,10,20,26)(5,14,16,27,22,25,18,33,15,31,32,34,17,9,23,24);(3,5,8,15)(4,9)(6,18,21,23)(7,22,19,17)(10,14)(11,27)(12,31)(13,25)(16,20,32,30)(24,28)(26,33)(29,34)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 4943);