Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C24 |
| direct product | C73×#24986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C73 |
| socle | C2×C73 | #2420 |
| prime radical | C73×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ G | |
642 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)(3,14)(4,18)(5,9)(6,23)(7,12)(8,13)(10,21)(11,17)(15,24)(16,25)(19,26)(20,28)(22,27)(29,30)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,6,5,8,17,7,16)(2,9,12,14,13,25,23,11)(4,19,21,15,22,30,20,31)(10,26,18,32,28,29,27,24);(1,4)(2,10)(3,15)(5,19)(6,20)(7,21)(8,22)(9,24)(11,26)(12,27)(13,28)(14,29)(16,30)(17,31)(18,23)(25,32);(1,5,6,17,8,16,7,3)(2,11,12,9,13,14,23,25)(4,19,20,31,22,30,21,15)(10,26,27,24,28,29,18,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 17974);