Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2398 |
| prime radical | #575×C73 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C8×C73 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 4 generators on 105 points:
(1,2)(3,12,15,25)(4,9)(5,10)(6,20)(7,11)(8,16,22,13)(14,26,29,31)(17,23)(18,24)(19,30)(21,28,32,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(3,13,15,16)(4,17)(8,12,22,25)(9,23)(14,28,29,27)(18,19)(21,31,32,26)(24,30);(1,3)(2,8)(4,14)(5,13)(6,16)(7,15)(9,21)(10,25)(11,22)(12,20)(17,29)(18,27)(19,28)(23,32)(24,31)(26,30);(1,4,5,18,7,17,6,19)(2,9,10,24,11,23,20,30)(3,14,13,27,15,29,16,28)(8,21,25,31,22,32,12,26)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 16822);